Just back from a visit to Eze thus afternoon. A hill top town, very pretty. We drove the moyenne Corniche from Nice. You have to drive that or the upper or lower Corniches as well. Intended to get to Menton but a big traffic jam just after Eze made us turn round.
St Paul De Vence is another gorgeous hill top walled town but a bit Disney now with every shop virtually an art gallery. Still well worth a visit as is the Maeght Foundation art gallery. I put a pebble on Chagalle's tomb yesterday. There's a restaurant here, Le Colombe d'Or, where Picasso, Matisse, Chagalle's, et al paid for meals with paintings. The artworks are on the walls of the dining room to this day.
The riviera train is a great way of seeing all the small towns along the coast from Nice to Menton or even Italy.
I am currently staying in Vence just around the corner From Dick and the dog (Richard and Judy) so I am told and Andrew Neil has a gaffe here if you want to go (very) minor celebrity spotting.
Biot and Grasse are worth a visit too.
Cagnes Sur Mer is a much friendlier place than Nice in my opinion.
Villefranche Sur Mer is a secluded deep water bay that is deep enough for US navy ships to visit. It has a fascinating history to find out about.
Antibes has a great Picasso museum, and Graham Green's flat, which looks just like one you'd see in Wythenshawe, has a plaque to announce its provenance.
You should get to some vineyards to sample the rose and buy some to take home.
I don't know your travel plans but if you are stopping over on the way down the Ibis Styles hotels are consistently good and very reasonable. Some of the other brands are bloody awful!