What is Cap Ferrat? A wooded peninsula of the French Riviera, the cape – according to several luxury estate agents – is now the most costly land in the world, ahead of even the priciest parts of Hong Kong, New York and London. In this haven of luminous sunlight, verdant tree cover and azure sea views, villas cost anywhere between €4 million (HK$35 million) and €200 million, according to Savills.

What sets it apart from the rest of the riviera? Location, seclusion and climate. Cap Ferrat holds a key position between Monaco and Nice, the two biggest riviera cities, with Nice international airport within easy reach – but it lies off the main coastal road in a cloistered world of its own. Cap Ferrat is balmy even in winter, and is wafted by cooling sea breezes from three sides in the heat of summer. The builders of the Grand-Hôtel in 1908 knew they had a sweet spot.

So how grand is this grand hotel? Dazzlingly white and presiding over extensive grounds with palm trees, exotic succulents and baize lawns, the hotel, like a classic ocean liner, sails effortlessly towards the cobalt sea that laps its far end. Acquired by the Four Seasons group last summer, this grande dame of seaside palaces is set fair for a future as glamorous as its storied past, in which it welcomed figures such as Winston Churchill, Pablo Picasso, Elizabeth Taylor and Paul McCartney.

Tell me more. Interiors are elegantly understated and white predominates, with cream-and-white marble and furnishings giving way to the occasional touch of colour: a Murano glass chandelier here, a vibrant tapestry there. A separate modern wing etched into the hillside is all tumbling vegetation and curvaceous lines, featuring suites that open onto spacious balconies or private plunge pools, all with sea views.

What about those gardens? Yes, they are special. Seven hectares of lush greenery slope down towards cypress-lined terrace walks and vine-hung loggias overlooking the sea, from where a funicular spirits guests down to the hotel’s Olympic-length infinity pool. Set by the rocky shore and filled with heated seawater, the Club Dauphin pool has been presided over since 1950 by Pierre Grüneberg, swimming instructor to the stars (among them Robin Williams, Brigitte Bardot and the infant Stella McCartney), now a sprightly 84.

Anything to eat? Club Dauphin offers refreshments by the pool and La Veranda all-day casual dining, but the big treat is the Michelin-starred Le Cap restaurant, with its Mediterranean cuisine. The wine cellar holds spectacular collections of vintage Château d’Yquem and Château Lafite Rothschild.

Who should stay, and who should not? The moneyed who like hushed tones, pristine elegance and discreet hideaways will be very comfortable. Anyone looking for a buzzing, hip scene will be down in the dumps. Winter holidaymakers can forget it, too: the hotel is closed from December to February.

What’s the bottom line? The 74 room choices at what is formally known as Grand-Hôtel du Cap-Ferrat, A Four Seasons Hotel include 24 suites, eight of them with their own pools, and an exclusive villa. Rooms start at €640 per night (including breakfast), the villa costs an arm and a leg. Visit www.fourseasons.com/capferrat.