Cap d'Antibes, millionaire's playground in the French Riviera: Where you can like a 1950s movie star

I swing my rental car through wrought-iron gates and onto a cobbled driveway shaded by palm trees and lined with terracotta pots of scarlet fuchsia. I drop my car keys into a waiting porter's hand, raise my sunglasses, and squint at the Imperial Garoupe, with its peach walls and bee-buzzed flowerbeds. The Mediterranean sun is hot on my face, and I feel like Gregory Peck.

Cap d'Antibes still retains a 1950s chic on a Riviera which, in many places, is living on reputation but overrun by concrete and mass tourism. This little cape 20 minutes out of Nice, however, remains exclusive. Villas nestle behind oleander hedges and movie stars stay in its discreet hotels during the Cannes Film Festival. Cap d'Antibes still has the bougainvillea, terracotta roofs and cheerful wooden fishing boats that once inspired 19th century painters. The rocky pine-scented coastline is beautiful, and much of it accessible to the public. The sun beats gold on hot summer days, setting the cicadas chirping and sunbathers wading topless into the aquamarine water.

F. Scott Fitzgerald, who famously wrote in The Great Gatsby that the rich are different, was one of several writers and artists that created the French Riviera's name in the 1920s as a playground for the famous and feckless, who came to drink gin, skinny-dip and play jazz records on their gramophones. The Hotel Imperial Garoupe, however, feels more 1950s, when the likes of Elizabeth Taylor and Audrey Hepburn stayed in Cap d'Antibes. The hotel was once a private villa and still feels like one, surrounded by olive trees and lawns, and reflected in a mosaic-blue swimming pool.

In the morning I have breakfast in a shady courtyard where banana trees erupt and a fountain splashes. Hovering waiters are quick to refill the coffeepot, and the Camembert cheese and pains au chocolat are an encouragement to gluttony. Then I follow a path through flowering shrubs to a wicker gate and onto the hotel's private beach where, over lunch, I tuck into seafood as I waggle my toes in the sand. The hotel's sands are adjacent to La Garoupe public beach, which features in Fitzgerald's superb novel Tender is the Night.

I walk for an hour around the low cliffs to "Billionaire's Bay" and back across the hill. At the summit of Cap d'Antibes a lighthouse offers brilliant views inland to the purple smudge of Provence and along the coast to the fortified, sea-beaten walls of Antibes. Beside the lighthouse, a chapel dedicated to mariners is hung with model ships and votive offerings. It seems a long way from the glitzy superficiality of nearby Monaco.

Of all the Riviera towns, Antibes retains its soul. Billionaires' yachts anchor in the harbour, but locals chatter in cafes, old men play boules beneath the trees and fishermen sell their catch in the Cours Massena each morning. When the fishermen are done the artists move into the covered market; then waiters take over at makeshift tables. It's easy to pretend I'm an old-time movie star here, drinking wine with foie gras on toast, un-harassed by the paparazzi that stalk today's celebrities through the flashy restaurants of Cannes.

Antibes was settled by the ancient Greeks, and Roman ruins lurk beneath its streets. The cathedral and seawalls date to the 13th century. Its pleasant sights also include the Picasso Museum, which features numerous sketches of Antibes. I watch a steady steam of brides decant from flower-decked cars outside the town hall, then rummage through the market on Place Nationale, whose "junk" includes Meissen teacups and escritoires.