Home to Anglophiles and blue bloods, Melbourne was Australia's political capital until Canberra was built in 1927, and its financial capital until the 1970s. But it was slowly overshadowed as Sydney's beauty, its harbor crowned by the opera house, began to draw the world's attention and money. For travelers, Sydney became the gateway to Australia. Even an Aussie prime minister, Paul Keating, declared, "If you're not living in Sydney, you're just camping out."

Proponents of Melbourne took these affronts with stoicism, remaining staunchly proud of the city's "authenticity" in the face of Sydney's shallow glamour. But on my own visits to Melbourne (always en route to somewhere else), I couldn't perceive any genuine threat to my hometown's exalted status. I beheld its boulevards down which San Francisco-style trams plowed, its grand Victorian buildings and parks, and the Yarra, such a muddy brown that people joked it flowed upside down. Melbourne did offer a certain understated "European" charm, to be sure, but it didn't compare with the brazen, slatternly allure of Sydney. I was happy to dismiss it as a staid and chilly relic—too conservative, too stuck up, too British. And what's worse, there were no decent beaches.

But something began to shift over the past decade, while I've been living in New York. Disturbing reports filtered to me that Melbourne was escaping second city syndrome back its mantle as the fashion, culinary, design, and arts capital of Australia. Sydney, it seems, is now so expensive and crowded that Aussie bohemians are flocking south: The more affordable, human-scale Melbourne has Australia's liveliest independent music scene, most inventive theater, and finest restaurants, exuding the feisty creative energy seen in other revived second cities like Glasgow, Antwerp, and Barcelona. Add ing insult to injury, the Economist Intelligence Unit—a business-consultancy group—ranked Melbourne "the world's most liveable city" in 2011 and again in 2012.

Had Melbourne actually become cool? The final straw came when the co-owner of my favorite coffee shop in downtown Manhattan, La Colombe, reported that his business partner was in Australia checking out the café scene. "I hear that Melbourne is the place to be right now," he confided.

And so I found myself staggering from Tullamarine Airport as Melbourne braced for a summer heat wave. "European" the city may be, but there was no mistaking that this was the Antipodes. The route into the city cut across rolling farm country, and on the radio there was talk of an invasion of kangaroos from the bush. I couldn't believe it (the classic misconception Americans have of Australia is that it's crawling with marsupials). "There's a 'roo jumping down the Calder Freeway," barked the host, "so be careful driving!" And Aussie art was everywhere: I checked into the hip Olsen, part of the new Art Series hotel group, whose walls are adorned with abstracted landscapes by local legend John Olsen (his paintings of the ocher earth resemble aerial photographs of the Outback). Piles of books offered a crash course in local creativity, from Aboriginal painting on.

It wasn't hard to notice that Melbourne had changed its look. There were new developments, as well as parks by the Yarra River that were drawing kayakers and bicyclists. A plaza had risen at Federation Square, with soaring atriums rising like enormous silver crystals. On the inner-city grid of Bourke and Collins streets, café tables spilled out over the sidewalks. It was all rather pleasant. Maybe it is the world's most liveable city. But does that make it exciting?

I needed some local authority to penetrate Melbourne's mysteries. Luckily, I had the opportunity to meet the city's most famous resident, Geoffrey Rush.