And so it has. Down by the harbour, in a triangle of land between the sea, the castle hill and Boulevard Jean-Jaures, is the old part of Nice, which dates from the 14th century. Sensitively restored and cleaned-up, its maze of narrow lanes is a fascinating place to wander; Picasso loved it here. The five-storey buildings are painted all the colours of the south - faded ochre, pale yellow, pink - with wooden shutters in delicately contrasting green or pale blue or white. Metal balconies, just large enough for a few pots of geraniums or herbs, cling precariously to the facades.
Gentrification has gone only so far. People still live here, and they hang the washing out of their windows on racks as they have long done. There may be tiny art galleries and places selling all manner of Provencal- print kitchen items, but there are also plenty of useful shops. Each morning the walk from my hotel took me past a butcher's shop with chickens roasting on spits outside, a scruffy North African cafe that sold halva and fiery egg dishes, a cafe that also sold newspapers, and several greengrocers whose gleaming displays made the mouth water. There was even a horse- meat butcher with a gloriously old-fashioned sign. Down the road, another shop was piled with dried herbs and spices - such as peppercorns mixed with tiny pink rosebuds, for grinding on to lamb - and just next to the hotel was a daily fish market, whose pungent smell never quite faded completely.
Cours Saleya, not far from these, is home to a flower market, a general food market (all those wonderful cheeses and olives), and a collection of fine cafes and seafood restaurants with terraces ranged along the sides of the narrow square. Here the art of idling usefully has been perfected; you can sit around on some terrace or other for ages watching the world go by and soaking up the atmosphere, and at a time of year when you wouldn't even have cast a clout if you'd been back in Britain.
Back in the lanes, there is more to see: several Baroque churches; the 17th-century Sainte Reparate cathedral, whose dome gleams with emerald- coloured tiles; and the Palais Lascaris, built in 1648, which is now a small museum.
Above the old town looms the castle hill, though there is no castle there now. Instead there's a cool and breezy park with Roman ruins, waterfalls and outdoor cafes, and a magnificent view over the sea and the small harbour. Hours can drift away as you amble happily round the park, then down the hill to the cemetery packed with extravagant, ornate marble monuments to past inhabitants, and back into the tiny lanes below.
After a few days in old Nice, the rest of the city - though undoubtedly prosperous and with some fine buildings - seems rather, well, bland. Not so Cimiez, now a wealthy suburb of Nice, which was once a thriving Roman city of 20,000 inhabitants. At the archaeological museum, I wandered round the ruins for hours until the need for shade, even in the spring, drove me into the cool and airy Musee Matisse to gaze at paintings, drawings and an extraordinary collection of Fauvist ceramics. In the park outside, an old olive grove, people dozed or picnicked under the trees, and a group of old men played boules.
Later I ambled down avenues with names such as Miles Davis and Dizzy Gillespie (Cimiez hosts an annual jazz festival) towards the Franciscan monastery. It was a perfectly clear day, so instead of going into the church I sat under an arbour and watched art students sketching the view. From up here everything looked tiny except the sea; old Nice was just a smudge at the foot of a rocky outcrop.
Matisse is buried up here; so is Raoul Dufy. And half-way down the hill is the statuesque Queen Victoria. She is neither part of the life and bustle of the old town nor the tranquillity of Cimiez. No wonder she looks so unamusedn
Air: Flying there has become tougher since both Air France and Air UK dropped their services from London to Nice. At present the lowest fares are available on EasyJet (01582 445566) from Luton, which charges between pounds 105.70 and pounds 165.70, including tax. British Midland (0345 554554) and British Airways (0345 222111) each fly from Heathrow. Of the two, British Midland has the lower fare, pounds 156.50, if you do not intend to travel in both directions on a Friday, Saturday or Sunday - when a pounds 10 supplement applies. BA has a base fare of pounds 165.50, and a weekend supplement of pounds 5 each way.
Rail: Eurostar trains from London Waterloo connect at Paris with TGVs to Nice (though you have to change stations in the French capital). The total journey time is around 11 hours. The return fare, if you stay a Saturday night, is pounds 109. It can be booked through BR International (0171 834 2345) and the Rail Shop (0990 300003 or 0990 717273), though the telephone queuing system that the latter uses can be extremely slow.
Staying there: Claire Gervat stayed at the Hotel Saint-Francois in old Nice (00 33 4 93 85 88 69), one of only a handful in the quarter. She paid F82 (pounds 9) a night for a single room with shared bathroom.
More information: French Government Tourist Office, 178 Piccadilly, London W1V 0AL (0891 244123). In Nice, there are tourist offices at the airport, next to the main railway station, and beside the Albert 1 gardens. The next Cimiez jazz festival will take place from 11 to 20 July.