Although scholars can't pinpoint when the first Polynesians set foot in the southeastern region of Oahu now known as Honolulu, oral histories and artefacts suggest there was a settlement there as early as the 12th century.

Honolulu means ‘protected bay', which aptly describes the calm, deepwater harbour that borders it. British captain, James Cook, who is credited with discovering Hawaii for the Western world in 1778, sailed by Oahu in the night on that fateful journey, entirely missing the bay and the little fishing village that stood beside it.

Sixteen years later, another English seaman, Captain William Brown, came upon the bay and dubbed it Fair Haven, echoing the Hawaiians' name for it.

When word spread about Brown's discovery, traders were ecstatic. They soon were dropping anchor in the large, safe bay by the hundreds, and the once-peaceful fishing village grew into a bustling seaport, then the capital of the Hawaiian kingdom in 1845, the capital of the territory of Hawaii in 1898 and finally, the capital of the state of Hawaii in 1959.

Honolulu today is a sophisticated, cosmopolitan city that's the hub of business, politics, education, entertainment and the arts in Hawaii. Fine dining, resorts, theatre, museums, concerts, shopping, sports, nightlife and cultural events – it offers all the pleasures of a world-class destination with the blessed bonus of balmy weather year round.

Start your visit in the city proper and then venture to other areas of Oahu. There are wonderful discoveries to be made everywhere you go, every day you are there.

Fondly known as the Bayou City, once nicknamed Space City, and widely recognised as the energy capital of the world, Houston was founded in 1836 (by brothers Augustus and John Allen) on the banks of Buffalo Bayou (a creek). This southeast Texan city is named after General Sam Houston, of the Texas Army that won independence from Mexico.

Within a year of its foundation, Houston became the capital of the Republic of Texas until 1840, when that honour was transferred to Austin. However, this Republic was rather short-lived as Texas joined the Union in 1845.

Despite its high-rise skyline, Houston has an open feel with several lakes and waterways (such as the Buffalo Bayou) winding their way through the city, surrounded by lush green landscape.

The city has been a dynamic centre of business, particularly in oil, since 'black gold' was discovered at nearby Beaumont in 1901. It is also the leader in space technology – Houston is home to NASA and the Johnson Space Center, the base for Mission Control and the place where astronauts are trained. It was established in 1961, as NASA's primary site for the design, development and testing of spacecraft for human flight.

The port area, which is linked to the city by the Houston Ship Channel, an 80km (50-mile) inland waterway, is thriving and has developed into an important business district for the city.  

The city is now the fourth largest in America, covering an area of 1600 sq km (618 sq miles).

In recent years, Houston's Downtown has undergone a dramatic transformation into a dynamic area of the city. It's now both an entertainment and residential district, and many buildings have been converted into loft apartments that sell at a premium.

The area is a magnet for people who wish to have dinner, see a movie or a show and walk along the historic waterfront in Sesquicentennial Park and on the Sabine-to-Bagby Promenade. Bayou Place, an entertainment complex in the Downtown Theater District, has been a great addition to the area, providing restaurants, live music and a multiplex cinema.

Houston has a temperate climate all year round, although the humidity in the height of summer can make the city feel warmer than the actual temperature. Such a climate means lush green gardens, fragrant flowers and towering trees.

Few cities bring to mind such images of sheer excess as Las Vegas. Located in the middle of the arid Mojave Desert, at the southern tip of the state of Nevada, Las Vegas is an oasis of life, energy and money – a city whose raison d’être is entertainment.

Over 35 million people visit Las Vegas year round, staying in the city’s 150,000 hotel rooms. According to the Las Vegas Chamber of Commerce, Las Vegas is now the fastest growing city in North America with an estimated two acres of land being developed every 24 hours, and seeing approximately 50,000 people annually choosing to make the city and suburbs their home.

Ironically, Las Vegas’ beginnings were, if anything, humble. In the 18th century, the spot where the city now stands earned the named Las Vegas (Spanish for ‘The Plains’), because of a natural spring that created greenery in the dry desert. The city itself was founded in 1905 (as a stopover on the Union Pacific railway between Los Angeles and Salt Lake City) but it remained a remote backwater until the 1930s.

In 1931, however, gambling was made legal and Las Vegas quickly began to assume its present character. At first, it drew the droves of workers building the nearby Hoover Dam. Soon, it became a gambling and vacation mecca for the entire country – it attracted stars like Frank Sinatra, Elvis and Liberace and became America’s premier entertainment hub.

The 1990s saw a trend towards building enormous hotel complexes competing with one another for the title of largest hotel in the world, and it has not let up to this day. The competition was won by the city-like MGM Grand, whose capacity of over 5,000 rooms has yet to be bettered, although the Bellagio, the Wynn Las Vegas and the newly opened Palazzo have certainly raised the bar in terms of lavish luxury and unchecked hedonism.

Today, Las Vegas is booming like never before. Entertainment so dominates Las Vegas that it is the backbone of the city’s economy, creating vibrant hotel, retail and hospitality industries. The city’s sheer exuberance in attracting visitors has created something along the lines of a city-sized theme park. Its residents lead normal lives in normal suburbs, but to visitors, it is an endless playground of neon lights, hotel lounges, topless revues, live entertainment and casinos.

By 2010, the face of the Strip is expected to be completely transformed following the completion of Project CityCenter and Echelon Place, two multiple high-rise, mixed-use residential and commercial developments that will boast the latest in contemporary urban design and architecture.

Los Angeles is the USA’s second largest city after New York. It has been called everything from La La Land to Tinseltown but is most commonly known simply as LA. Sprawling along the Pacific coast of southern California, its coastline stretches 122km (76 miles) from Malibu to Long Beach. Inland, the city fills a vast, flat and once arid basin ringed by the Santa Monica and San Gabriel mountains.

Arriving by plane gives a good first impression. Out of this vast flat grid of streets and buildings rises a cluster of imposing skyscrapers. These mark Downtown, 26km (16 miles) inland from the coast. Northeast is Pasadena. To the west and northwest are Hollywood, Beverly Hills and Century City and the wide San Fernando Valley. To the south is Long Beach. Along the west coast are Santa Monica, Venice Beach and Marina del Rey.

Founded in 1781 by Mexican settlers, over the centuries, LA grew from a cow town to a Gold Rush boomtown to an oil town. In the 1920s, the fledgling film industry decamped from New York in search of sunshine and Hollywood was born. Today, all the major studios are here and the city is the world’s undisputed king of film-making.

Disneyland may be the city’s major attraction, but LA is also home to world-renowned cultural institutions from the Museum of Contemporary Art to the LA Philharmonic and the stunning Getty Museum.

LA is exuberant – there are few places in the world where the phrase ‘Express Yourself’ is taken so literally. Hippy health fanatics exist happily alongside some of the most glamorous and wealthy people in the world. Most visitors come to enjoy world-class shops and restaurants, lie on beaches bathed in almost constant sunshine and simply to people watch.

Set high on the eastern bank of the mighty Mississippi River, in the southwestern corner of Tennessee, Memphis is known the world over as an immensely musical city – the cradle of the blues, the birthplace of rock ‘n’ roll and the location of Graceland, Elvis Presley’s flamboyant mansion.

However, there is much more to Memphis than music. Named after the capital of ancient Egypt (a reference to the Mississippi being the Nile of America) this city is a hustler, an enterprising metropolis with trade running through its veins.

There is evidence that its origins as a settlement date back to at least AD1000, when Native Americans lived and worshipped here. The modern town was founded in 1819, after its strategic position, high enough above the river to escape flooding, had attracted the attention of European settlers.

A natural crossroads between New Orleans, St Louis and Chicago, Memphis became an important trading centre in the mid 19th century and the main shipping port for cotton grown in the Mississippi Delta. Its climate is not inhospitable (although summers are hot and humid, the winters are generally mild) and the city soon grew, spreading eastwards from the river.

Today, Memphis is an intriguing mix of old and new, with shabby warehouses and serene Victorian villas jostling for space with modern skyscrapers and gleaming shopping malls. Construction is booming, and a striking new landmark building is planned to house retail and office space, a hotel and restaurants. The work ethic is strong and the city is home to many contemporary companies, although traditional industries are still important – as evidenced by the cotton exchanges in the Downtown area, which are still at the heart of the world cotton trade.

It was cotton that indirectly spawned the Memphis music industry, as the blues evolved from songs sung by slaves working in the cotton fields. After the Civil War, rural black people flocked to the city in search of work. Beale Street in Downtown Memphis became the centre of black life and culture and the sound of the blues soon oozed from almost every building.

Today, Beale Street is still a musical mecca, a vibrant place where bands play in smoky bars, locals and tourists stroll on sultry summer evenings and young boys perform breathtaking backflips along the street.

The laid-back atmosphere of the city, as characterised by the local saying: ‘it’s cooler in the shade’, has often concealed a rougher edge. Memphis was the setting for tragedy in 1968, when black civil rights leader Dr Martin Luther King was assassinated on the balcony of the Lorraine Motel. Tension increased, residents left for the safety of the suburbs and Downtown fell into a seemingly terminal decline.

However, the city has risen from the ashes of hatred. The Lorraine Motel is now America’s Civil Rights Museum and millions of dollars are being spent on revitalising the Downtown area. Developers are transforming derelict warehouses into trendy loft apartments, condos, art galleries and boutiques.

New museums and stylish restaurants are springing up and the expansive FedExForum, opened in 2004, is the area’s premiere sports and entertainment complex. The culture has always been music-oriented, and 2007 marked the 30th anniversary of Elvis’s death and 50 years of soul. Even the blues, written about someone else’s struggles, makes listeners feel toe-tappin’ good, in this diverse, vibrant and family-friendly city brimming with southern charm. Memphians celebrate their roots soul-deep.

They’re still making legends in Memphis and the music will continue to evolve, reflecting the times, even while the Mississippi River still rolls on to the Gulf and The Peabody ducks (see Further Distractions)  march precisely at 1100 and 1700.

Past and present sit side-by-side in sprawling Mexico City where a handsome historic Colonial-era heart sits amongst ever-changing modernity.

Settled by the Aztecs in the 14th century before being overthrown by the Spanish, Mexico City was founded by the conquistadors on Lake Texcoco in 1525. Today, the capital is known affectionately as ‘el DF’ (day-effay) by proud locals and is home to a hip, emerging art and gastronomic scene that is drawing a new wave of trendy elite to its fashionable tree-lined neighbourhoods.

Mexico’s chaotic capital city is one of the most vibrant urban spaces in the world. Huge expanses of metropolitan parkland represent the largest on the planet while gorgeous upscale pedestrian-friendly districts are dubbed the Beverly Hills of Mexico.

Brightly-painted, open-topped barges (trajineras) trawl Mexico City’s mysterious ancient canal system past “floating islands” (chinampas) piled high with flowers, fruits and vegetables.

Although Mexico City has its foibles, annoyances and frustrations, it remains one of the world’s most exhilarating and exciting metropolitan hubs.

Miami is almost more Latin American than simply American – famed for its sunny weather, savoir faire, legendary party scene and super-cool South Beach style.

Miami and its neighbouring city Miami Beach are cities are emotion, colour and texture. Much of Miami’s appeal is due to its diverse neighbourhoods, which range from towering skyscrapers in downtown Miami (the commercial heart of the city) to Little Havana, home to the Cuban community. Meanwhile, the Port of Miami is the world’s largest cruise port.

Miami Beach is world-renowned for its ‘gold coast’ hotel strip, palatial properties and exceptional outdoor recreational facilities. Its glamorous, see-and-be-seen South Beach neighbourhood is instantly recognisable, with its candy-coloured art deco buildings set against a pure South Florida backdrop of cloudless skies, dazzling blue ocean, pale sandy beaches and swaying palm trees.

Thanks to its warm weather year-round, both cities share one ethos: life here is not about work but plenty of play.

Spreading out from the banks of the Mississippi River, in the north-central US state of Minnesota, Minneapolis and St Paul are colloquially known as the Twin Cities.

With striking contemporary buildings, Minneapolis is the more cosmopolitan of the twins. St Paul, with its many restored 19th- and early 20th-century buildings and laid back attitude is more like a small town. Both are veritable melting pots with significant Hmong and Somali populations among its residents.

With 949 of Minnesota’s 12,000 lakes lying within the metro area, outdoor recreation is a given. Both cities are rich in the arts and cultural entertainment. The quality, quantity and diversity of productions and facilities far surpass the norm for cities of this size, with The Walker Art Center and Guthrie Theater among the top cultural venues in the nation.

Montreal (Montréal) is unique in North America, blending a brash New World urbanity with the romantic charm of its European-flavoured historic districts and a Gallic sense of joie de vivre evident in the city’s many pavement cafes and dynamic nightlife.

Although its downtown skyscrapers are a testament to the economic clout of Canada’s second largest city, visitors are more likely to be drawn by the promise of a horse-drawn calèche ride along the cobbled streets of Old Montreal or a stroll up Mount Royal, the city’s landmark.

Montreal is situated on an island, 50km by 16km (31 miles by 10 miles), between the Rivière des Prairies and the St Lawrence River. ‘Discovered’ by Jacques Cartier in 1535, the island was already inhabited – the Iroquois village of Hochelaga stood at the foot of Mount Royal. By 1642, Hochelaga was abandoned in favour of the European settlement, Ville Marie.

A French colony until 1760, Montreal fell to the British, and today some 67% of the inhabitants claim French as a mother tongue, making Montréal the second most populous French-speaking city in the world after Paris.

Defying simple definition, Montreal’s character is rooted within the uneasy marriage of the founding French Catholic and English Protestant cultures yet derives its vitality from a cosmopolitan mix of immigrants from around the globe.

The charming buildings of Old Montreal, are today filled with boutiques, bars, hotels and restaurants and from the promenade along the adjacent Old Port one sees the nearby islands of Ile Ste-Hélène and Ile Notre-Dame, site of the Expo 67 World Fair, and now comprising the city’s largest park, Parc Jean-Drapeau. The world’s tallest inclined tower can be visited atop the Olympic Stadium, a legacy of the 1976 Summer Olympics, and next door is the city’s expansive Botanical Garden.

The ‘real’ Montreal, though, exists in its neighbourhoods – like Little Italy and Chinatown and especially the multicultural Mile End and Plateau Mont-Royal. Boulevard St-Laurent (‘The Main’) bisects Montreal into east and west, is the city’s liveliest street, where the shops, bars and ethnic restaurants draw crowds until well into the night.

The best time to visit Montreal is in the summer, when even the nights can be sultry and the whole city seems to be partying, as the festival season (notably the Festival International de Jazz de Montréal) moves into high gear. The cooler autumns bring out the colours in the leaves and are a great time to visit the forested Laurentians or the rolling hills of the Eastern Townships. Even the cold and snowy winters can be enjoyable – the city authorities maintain more than 150 skating rinks in the region every winter where everyone can enjoy Montréal’s winter charms.

New Orleans is the jewel of the southern US state of Louisiana, sparkling just above the mouth of the mighty Mississippi River where it meets the Gulf of Mexico.

The heart of the city lies between the river and Lake Pontchartrain and, from this approximately 13km (8-mile) core, the suburbs of Greater New Orleans spread out into the surrounding expanse of drained swampland.

The river's shape, as it curves around the central district, gave rise to the city's nickname, ‘Crescent City', although, New Orleans is more likely to be known as the ‘Big Easy', a clue to the city's laid-back and genial atmosphere.

The subtropical weather is generally hot and humid from mid March to October, with summer bringing intense afternoon thunderstorms, although winter can be chilly and damp.

On 29 August 2005, Hurricane Katrina came roaring through the Crescent City, with devastating flooding the result. Though tourist areas like the French Quarter remain intact, some mimes, musicians, jugglers and other street performers (those that lent so much charm to the area) have not returned. The lovely Garden District has recovered nicely, but signs of destruction remain visible in many other areas and the healing process is very, very slow. In conversations heard around town, terms like ‘pre-K' and ‘post-K' have become part of the vernacular.

New Orleans was founded in 1718, at the swampy foot of France's huge Louisiana territory, and named after the Duc d'Orléans. Despite hurricanes, mosquitoes, disease and floods, settlers came and the city prospered. In 1762, the territory was secretly ceded to Spain.

Drawn by the rich plantations and thriving port, the Americans came seeking their fortunes. During the 19th century, New Orleans boomed with trade from the cotton and sugar plantations and, by 1860, was the wealthiest city in the country. After the Civil War (1861-65), the region's slave-based agricultural economy declined.

New Orleans, with its unique atmosphere, is one of the most popular US destinations, particularly during its magnificent Mardi Gras celebration in late February or early March.

The mixing of French, Spanish, African and American cultures over the centuries has created a unique environment, blending the genteel elegance of the colonial Creoles, the music and cuisine of the peasant Cajuns, the exuberance of Mardi Gras, a touch of voodoo and a big dollop of Dixieland jazz.

The timelessness of New Orleans can be heard in the clattering of the streetcars, the distant whistles of the riverboats, a busker playing a saxophone or the soft sounds of jazz through an open window.

Its oldest district, the French Quarter (Vieux Carré), has a wealth of architecture that portrays its colourful history. Most of the original buildings were destroyed in the fire of 1788 and the graceful houses with ornate wrought-iron balconies are actually Spanish in style. In fact, New Orleans has 17 National Historic Districts, with more than 35,000 listed buildings.

Music and the city's famous gastronomy attract visitors from all over the world. Many venues have reopened and most have returned to regular operating hours. As they say in New Orleans, ‘Laissez les bons temps rouler' – let the good times roll!