In 1913, Jewish immigrants Joe and Jennie Weiss began selling snacks, such as local favourite stone crab, from their front porch, a couple of blocks from the beach. Today, the bathing casinos have gone but there is still a Joe's Stone Crab, complete with the Weiss' granddaughter, Jo Ann Bass, an elegant octogenarian, buzzing about the restaurant.

In the original dining room there are chandeliers from 1931, etched glass windows and a black-and-white mural of Joe and Jennie. Bones, the maitre d', has been working here for 47 years, and some of the diners have been coming for just as long. Although the menu has been stylishly updated, it still lists some classics. I pass on the liver and onions and opt for the stone crab, on the advice of Bass, whose father, she laughs, "knew every mobster in the city".

The rotunda of the old Post Office, a couple of kilometres from Joe's Stone Crab, is an example of Depression-Modern architecture. A dramatic mural of a mythologised Floridian history sweeps around the top of the circular space, above rows of still-used brass mailboxes. The cool marble interior offers respite from the heat, even for those without letters to mail.

Municipal buildings, however, are not the architectural celebrities of Miami Beach's halcyon history. The 1920s and 30s attracted millionaires who built fantastic, opulent estates.

The Mediterranean revival (a mash-up of Spanish, Italian, Moorish and French influences) Vanderbilt Mansion, on Fisher Island, is a legacy of Carl Fisher, an early promoter of swampland real estate. Its Napoleon period walnut-panelled rooms, snooker parlour, grand ballroom and nearby cottages were a playground for Vanderbilt's family and friends, the tycoons of the United States' Gilded Age. These facilities are now enjoyed by guests of the exclusive Fisher Island Hotel & Resort.

In 1930, Alden Freeman, a Standard Oil trust-fund baby, built Casa Casuarina, which channels the grandeur of the Santo Domingo home of the son of Christopher Columbus. Fashion designer Gianni Versace bought the property in 1992 and rescued it from disrepair. Five years later, he was murdered in front of what had come to be known as Versace Mansion.

A short stroll from the mansion's coral and limestone terrace, past a bronze Aphrodite, is an elaborately tiled inner courtyard lined with a succession of arches. A series of narrow, internal staircases brings guests of the hotel - for that is what the mansion now is - to an observatory. From here, you can peer at the stars, the sea or iconic Ocean Drive, which is lined with art-deco hotels, Miami Beach's architectural jewels.

The Essex House Hotel's white façade, horizontal banding, porthole windows and neon spire evoke a luxury ocean liner. Inside, above a curved fireplace, is an Earl LaPan faux-marble mural depicting the Everglades, in Florida, complete with an alligator. To the right of the lobby's scagliola fireplace, a pattern can be discerned in the terrazzo floor - it's an arrow that once pointed to a secret gambling room; gangster Al Capone and "the boys" are reputed to have played cards here.

In the 30s and 40s, haute venues, such as the Copacabana, had bevies of chorus girls, and headliners including Sammy Davis Jnr. Those nightspots are long shuttered but Mac's Club Deuce, the city's oldest bar, is still in business.

"It's lost its pizzazz," sighs my hotel's concierge. But the 90-year-old bar still has character - and characters.

"We just sit around and shoot the bull and make up stories," laughs long-time regular Sergio Bonilla, perched on his favourite stool at the long, oval bar. Other punters play pool and spin jukebox tunes in the blinking neon light. The exhilarating diveyness takes me back to the time when mob underlings were the regulars.

The second world war put a pause on hedonism, and Miami Beach became what has been described as "the most beautiful boot camp in America" for thousands of soldiers. Hotels morphed into barracks and restaurants into mess halls. By the 50s, many of those same soldiers were holidaying at the town's lavish new resort hotels, such as the Eden Roc and Fontainebleau.

"They started a whole new era," says Miami historian Arva Moore Parks. It was a time of cha-cha and rumba, and a whole new style of architecture. Miami Modernist, or MiMo, was a response to a newly affluent population's demand for extravagance and glamour, and boasted buildings with air conditioning, balconies, views of the sea and, most importantly for the guests, grand lobbies. Curved walls, wing-shaped motifs representing flight, mosaic tiles and floating staircases all played their part.

Eden Roc was one of MiMo architect Morris Lapidus' finest creations, and its curvilinear exterior and latticework, Paris Metro-inspired lamps and turquoise mosaic tiles have all been beautifully preserved. The sweeping stairs were designed so bejewelled women could make a dramatic entrance into a lobby that still has towering gold-leafed columns wrapped around an iconic oval-shaped quartz bar.

"Miami Beach was America's French Riviera in those days," says Madeleine Kirsh, the proprietor of C. Madeleine's, which sells period Miami outfits but is curated more like a museum than a shop.

She shows me an Oscar de La Renta hand-embroidered satin dress with a cape, surely designed for a sweeping staircase entrance. And then a Pucci cotton bathing suit with matching skirt - as perfect for the Eden Roc pool today as it would have been in the 50s.