At 4 million people, Sydney is the biggest and most cosmopolitan city in Australia. Take a taxi from Sydney Airport and chances are that the driver won't say "G'day" with the accent you might expect. Like the United States, Australia is a society of immigrants, and Sydney has been their preferred destination. Since the 1950s, the Anglo-Irish immigrants who made up the city's original population have been enriched by successive waves of Italians, Greeks, Turks, Lebanese, Chinese, Vietnamese, Thais, and Indonesians.

It's good to keep in mind that visiting Sydney is an essential part of an Australian experience, but the city is no more representative of Australia than Los Angeles is of the United States. Sydney has joined the ranks of the great cities whose characters are essentially international. What Sydney offers are style, sophistication, and good, no, great looks -- an exhilarating prelude to the continent at its back door.

Named after then-British Prime Minister Lord Melbourne, the city of 3½ million was founded in 1835 when the Englishman John Batman and a group of businessmen bought 243,000 hectares of land from the local Aborigines for a few trinkets. After gold was discovered in Victoria in the 1850s, Melbourne soon became the fastest-growing city in the British empire, and a number of its finer buildings were constructed during this period.

If, like its dowager namesake, Victoria is a little stuffy and old-fashioned, then the state capital of Melbourne is positively old world. For all the talk of Australia's egalitarian achievements, Melbourne society displays an almost European obsession with class. The city is the site of some of the nation's most prestigious schools and universities, and nowhere is it more important to have attended the right one. In a country whose convict ancestors are the frequent butt of jokes, Melburnians pride themselves on the fact that, unlike Sydney, their city was founded by free men and women who came to Victoria of their own accord.

Whatever appearances they maintain, Melburnians do love their sports, as evidenced by their successful bid to host the 2006 Commonwealth Games. The city is sports mad -- especially when it comes to the glorious, freewheeling Melbourne Cup horse race that brings the entire nation to a grinding halt. The city also comes alive during the Australian Tennis Open, one of the four tennis Grand Slam events, which is held every January at Melbourne Park.

For years Melbourne's city central region was seen as an inferior tourist attraction compared with Sydney's sparkling harbor. But a large-scale building development along the Yarra River in the early '90s transformed what was once an eyesore into a vibrant entertainment district known as Southgate. Starting from the charm of Alexandria Bridge behind Flinders Street Station, pedestrians can tour through Southgate's myriad bars, shops, and restaurants on the south side of the Yarra River. An assortment of unusual water displays farther along mark the entrance to the Southbank's brash Crown Casino, where gasoline-fueled towers shoot bursts of flames on the hour after dark.

Many changes have also taken place in the heart of the city, where Federation Square, a large civic landmark built in 2002, now houses a second branch of the National Gallery of Victoria, the Centre for the Moving Image, the Australian Racing Museum, the Melbourne Visitor Center, and an assortment of shops and restaurants.