Metaphor well serves a big city, with its great uproar of opinions and possibilities, the avenues of illusion, the ceaseless spectacle - as with the idea of melancholia in a city as big as Buenos Aires. Don't cry for me Argentina? I well nigh weep among her fallen angels.

It's in crisp Sunday morning light that I walk amid the dead at Cementerio de la Recoleta, through a labyrinth of Catholic crosses and sparse Latin and a string of fatal dates in the heart of the city. "The last surprise party of a dying class," is how local scribe Juan Jose Sebreli described this patrician graveyard and baroque marble fantasy. V.S. Naipaul called the must-see attraction a "mimic city".

I come here looking for a poem. It's by Jorge Luis Borges, the Argentinian oracle who once declared: "Buenos Aires is such a boundless city that nobody can know it." It's here, somewhere, on a bronze plaque on the Alvear family mausoleum and begins: "She once had everything but one by one/Each thing abandoned her. We saw her armed/With beauty."

These opening lines of love and death and forsaken dreams I think of as a story of the city. Of a place founded in 1536 by a Spanish aristocrat, on a river of silver, named after a patron saint of sailors - the Virgin of Buen Ayre - and feeling as eternal as air and water.

Fresh arum lilies and red roses lie by the tomb of Eva Peron and in the necropolis everywhere I turn I see beauty. Four days in Buenos Aires has this effect. And I've not yet set foot in a tango hall, nor watched from terraces the choreographed passion of their futbol.

"It's like Paris populated by Italians who speak Spanish," says Randy Provence of living in the world's 10th-biggest city. He's a friend of the friend I travel with, who moved here from California with his wife last year. "It's all of Europe, at the end of the Americas."

He takes us to La Boca, the former meat-packing barrio where Diego Maradona is a saint, tango is on the street and corrugated iron on Italian immigrants' houses wears the colours of adventure. We see La Bombonera ("the chocolate box"), a football stadium where the legendary Superclasico is played once a season between Boca Juniors and uptown rivals River Plate.

Our airport taxi driver told us already of this team. "Traffic here is crazy," were his first words. "La Boca, number one," his second. We smiled and nodded. At lights he reached over and pulled out a Boca shirt from the glove box, signed by Maradona, who last week was named coach of the national side. We arrived in the city with it draped on the dashboard like a magic totem. ("He can sell his house but not that shirt," says a restaurateur when I later recount the tale. "Football here is something very strong.")

Bruce Chatwin, the inveterate traveller, observed: "The history of Buenos Aires is written in its telephone book." It is a city of ports and immigrants, a melting pot on the muddy crosscurrents of the Rio de la Plata, filled with Iberians and Basques, Ligurians and Neopolitans, and Turks, Jews, Greeks, Dalmatians and the odd Welshman, too.

At Plaza de Mayo we start a walking tour with the story of the desaparecidos ("the disappeared") and the mothers who gather here each Thursday to mourn their loss. "It's hard, it's torn," says our guide, Aldana Cevina, 26, of a society divided still by the brutal past rule of a military junta. "The state was supposed to defend the people, not kill them."

Life sentences were handed down recently to two generals of the 1976-83 dictatorship. Bodies are buried under bridges. Long shadows of shared memory continue to fall on the city's sharp corners, on its grid of Beaux-Arts arcades and Spanish baroque Jesuit churches, and in the cobblestone streets of San Telmo, famous for its Sunday antique market and narrow, century-old conventillo ("small convent") tenements where port workers once lived.

We walk from La City to Montserrat and along the rejuvenated Puerto Madero and all the way I try to break a 100 peso note (about $48). It's the "small change crisis" and it tells of a greater lost fortune.

For much of the 20th century, Buenos Aires mixed in fine social circles, alongside Paris and New York as one of the world's most expensive cities. It's porteno inhabitants, the "people of the port", aspired to fur coats and jewels and a good life earned by trade from the pampas, the unerringly flat grasslands that spread from the city.

Then came "the crisis". The Argentinian peso, once pegged to the US dollar, plunged overnight in late 2001 to a low of nearly four to one, unhinged by runaway inflation and the world's greatest default on public debt. The country's finances collapsed. Banks were besieged. Savings hemorrhaged. Hard economic times? Buenos Aires knows them well.

But from adversity has come a new beginning. "Buenos Aires is an amazing city," says Inez Mendiera, a 29-year-old chef of Basque, Polish and Romanian ancestry, who, after cooking in kitchens around the world, returned recently to start a wine club with her partner in their own home. "I think we are in the right place in this part of the story."

Their club, Casa Coupage, is up a marble staircase and in the elegant rooms of their 1920s apartment. It serves baked sweetmeats with glasses of malbec and represents the creative esprit de corps that's gripped scruffy-chic barrios such as Palermo. "We really believe the energy in this city will be our breakfast," she says.

All has fallen around it but Buenos Aires is not bowed. Musicians, designers, writers and artists are drawn instead to its bohemia, cheap digs, European sensibilities and belle epoch boulevards of broken dreams. Director Francis Ford Coppola is the latest to succumb, using the city as a backdrop for his film Tetro, a drama that's washed the streets in gossip.

Travel writers say it's the new Prague. A report in the Buenos Aires Herald says the capital ranks 138 among 143 cities in a cost-of-living survey (topped, incidentally, by Moscow, Tokyo and London). Tourists arrive in record numbers, cashing in on a sensualist lifestyle and Latino nightlife all had on the cheap.

And now it is the turn of Australians. Qantas starts a non-stop service from Sydney to Buenos Aires this month. But after 13 hours and 10 minutes in the air, what can visitors expect in this city translated as "Fair Winds" or "Good Airs"?

In Manuel Montalban's novel, Quinteto de Buenos Aires, a man asks the gourmet detective, Pepe Carvalho, what he knows of the city. He answers: "Tango, the disappeared, Maradona."

In four days, my knowing becomes a longing. I think of it now as a city of sequins and stockinged legs on the tango floor, of oak-and-brass bars, Citroen 2CVs, asado barbecues, Che Guevara, joyous songs at the futbol, Evita Peron, belle arts, forged-iron windows, ornate architecture and a lingering sadness that comes from cultural displacement and lost riches and the tragic deaths of 323 men on the Argentine naval cruiser General Belgrano in the Falklands War.

On our last night a waiter pours a bottle of Torrontes, a spicy white, and likens it to the city: "You're going to love it or hate it but you'll never forget it."

Dugald Jellie stayed in Buenos Aires courtesy of Destino Argentina.