It's 8am on "Cape Celebrity", a tiny finger of rock that thrusts out suggestively into the marvellous Med and which, for the past 150 years, has played host to everyone from royalty to the Rolling Stones.
But this morning as I jog round the picturesque coastal path that virtually circumnavigates exclusive Cap Ferrat, there's a noticeable lack of the rich and famous.
Where is everyone? There's a couple of dog walkers and a few fisherman, but not even Bono (who has a home here) is to be seen.
Cap Ferrat – perfectly positioned between Nice and Monte Carlo – was once one of the most glamorous places of exile on the planet; a haunt of the well-known, the well-heeled and the frankly notorious.
Somerset Maugham described the French Riviera as "a sunny place for shady people". And he wrote from experience. From 1926 the novelist and playwright held court at illa Mauresque, one of Cap Ferrat's most stylish homes, where his homosexual lifestyle was less likely to cause a Wilde-like scandal. Even so, his guest list reads like a who's who of English literature: T. S. Eliot, H. G. Wells, Rudyard Kipling, Virginia Woolf, Evelyn Waugh and Winston Churchill.
Villa Mauresque was originally built to house the personal priest of King Leopold II of Belgium, a monarch with much to confess. Using his ill-gotten gains from raping the resources of the Belgian Congo, Leopold was among the first of Europe's mega-wealthy to spot the property potential of the peninsula. Until then Cap Ferrat had been the domain of impoverished fishermen and the occasional pirate.
The monarch snapped up most of the cape's western side, housing various mistresses in several grand villas reputedly connected by underground tunnels to his residence, Les Cedres.
Noel Coward – whose song I Went to a Marvellous Party parodied the Cap Ferrat crowd of the 1930s – was another Cap convert, performing at the five-star Grand-Hotel du Cap-Ferrat which remains one of the great Riviera establishments.
Today, although Cap Ferrat is said to be the most expensive real estate in the world after Monaco, most of its grand homes are hidden away behind high walls.
The most famous exception is La Fleur du Cap, a pink villa clinging to the waterfront at Place David Niven. Built in 1880 by the son of an arms dealer, the house originally known as Villa Socoglio has been home to the Duchess of Marlborough, King Leopold III, Charlie Chaplin and Niven. Briefly the villa even became a film star itself – used as a set for the Trail of the Pink Panther.
Strictly speaking, Villa Nellcote is in neighbouring Villefranche rather than Cap Ferrat but it is easily the area's most notorious address. A Gestapo headquarters during the Nazi occupation of France, the 16-room mansion was rented by Keith Richards when the Rolling Stones fled Britain for tax reasons. The band recorded their 1972 album Exile on Main Street in the mansion's basement – drug and sex-filled sessions which have gone down in rock'n'roll legend.
But don't think you need to be a millionaire to enjoy Cap Ferrat, especially if you visit in October as I did when the sun still shines warmly after the hordes have disappeared. A web search secured an inexpensive room with a balcony overlooking the pool at the pleasant Hotel La Villa Cap Ferrat in the heart of picturesque Saint Jean Cap Ferrat. Breakfast in the poolside pavilion was a particular highlight.
The only town on the peninsula, Saint Jean Cap Ferrat retains its character of a working fishing village, albeit an upmarket one. Restaurants, bars and cafes crowd around the old harbour.
Each of the cape's five public beaches is within easy stroll of the town, some offering diving, snorkelling and other water sports. There's also a series of walking trails including Le Tour Du Cap Ferrat, the seven-kilometre trail that takes you past the historic lighthouse and gives you unsurpassed views of the Bay of Angels.
Still, whatever your budget, visit Villa Ephrussi de Rothschild. Completed in 1912, it is an Italian Renaissance-inspired palace where no expense has been spared.
Poignantly, it's also a monument to Baroness Beatrice Ephrussi de Rothschild. An heir to the Rothschild banking family she was married at 19 to an older Russian friend of her parents. The marriage proved disastrous. Maurice Ephrussi, an inveterate gambler, gave her a sexual disease which prevented her having children.
Divorced in 1904 and inheriting her father's vast wealth, Beatrice built the villa to house her art collection, bequeathing it to the French Institute on her death in 1934.
The nine specially themed gardens alone are worth the admission. As you admire the musical fountains which burst forth every 20 minutes, allow yourself the fantasy of being mega-rich for a moment.
www.saintjeancapferrat-tourisme.fr/index.php?lang=en
Qantas and partner Emirates are among the airlines with regular flights between Nice and Sydney/Melbourne. See qantas.com.au.
Hotel La Villa Cap Ferrat has 20 rooms, some with balconies. Rooms from $210, see hotel-villa-cap-ferrat.com/gb/.
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