Arriving in Nice, at an airport that is within walking distance of the city centre, brings to mind Robert Louis Stevenson’s claim that the great thing is not to arrive, but to travel, ‘not to go anywhere but to go’. To be honest, arriving in Nice makes a nonsense of this, but RLS, no stranger himself to the French Riviera, was writing before the advent of budget air travel.

Nice is a city of contrasts and paradoxes. It is home to the wealthy and welcoming of the less wealthy. If you were on a very tight budget, you could just about stroll from the airport to the long, arcing Promenade des Anglais, its endless procession of joggers, roller-bladers, cyclists and walkers making it as lively as Central Park, but with sunshine and sea.

Our first stop is the Old City, with its narrow streets, baroque architecture, and famous Marché des Fleurs. But it had been an early start and a long morning: the hunger pangs are biting. ‘Pas de probleme.’ says our guide, Myriam. ‘We go to Chez Theresa’s.’

We find Theresa’s place in the main market square, at the end of the flower stalls. ‘Theresa is a real traditional Nice woman, an institution,’ explains Myriam, still grinning. ‘And she’s looking for a husband.’

Theresa, heavily made up and – a bit like parts of Nice – with an air of faded glamour about her, is standing over an enormous, sizzling copper hot plate. We seat ourselves around a plastic table and she heats up enormous pancakes, made with chickpea flour, water and olive oil, to concoct the local dish, the socca, which arrives every few minutes on the back of a motorbike. Having been fed, watered and entertained by Theresa, we take our leave and explore the other side of Nice: the suburbs.

Here, the architectural influences – Italian, Hindu, Oriental, Greek, Neoclassical, Renaissance – illustrate how far and wide the pull of the Riviera really was in the 19th century. These days, the influx has slowed to a trickle – a predominantly Russian trickle.

Yet Nice doesn’t feel like the exclusive playground of the wealthy. It’s vibrant and surprisingly affordable. From July the entrance to all the city’s many museums will be free, while a journey on the new tram (Edinburgh, take note) costs a single Euro.

If you’ve made all these savings on your transport, then a visit to the Chateau de la Chevre d’Or is in order, even if only to gawp. This boutique hotel, the ultimate in moneyed Nice sumptuousness, is slowly taking over the hilltop village of Eze. In this tiny village are two Michelin-starred restaurants (Nice has 25 in total), whose terraces offer mind-blowing views across the Cote d’Azur. ‘Down there,’ our host tells us, ‘you can see Bono’s house. And on the small peninsula is Elton John’s. Bono is a good customer of ours.’

A good customer, she confirms, rather than a regular one. So don’t be put off.

Richard flew to Nice with Easyjet. www.easyjet.com, flights from Edinburgh from £25.99 one-way (including tax), and £47.66 return. For more information on the Chateau de la Chevre d’Or, see www.chevredor.com