Museum of photography which sometimes has interesting exhibtions:
http://www.tpi-nice.org/
It's very near the Nice Etoile shopping centre, which is good if you are travelling with people who have less interest in photography!
ArtaPhoto has a nice collection (not for sale though!) of Leicas and Nikon cameras. Haven't managed to find any other camera shops of note yet!
Finocchio ice cream vendor in the old town is worth a stop. Huge selection of ice cream, including some weird flavours (tomato and basil! Beer flavour not so good. I like the lavender, the ginger and the chocolate and chilli pepper ones).
I like the Chagall Museum the best, Matisse Museum worth a visit also. Then you have the Picasso Museum in Antibes. Antibes is worth a visit. The walk around the Cap d'Antibes is very nice. You might get a look at the security wall of Abramovich's mansion too. Also in Antibes you can look at the super yachts in the harbour. There is a car park beside the Napoleonic era fort (Fort Carre - has guided tours, quite interesting). There is a free shuttle bus from there into the town if you want to safe on parking and traffic. Antibes has a nice but crowded sandy beach. More beaches further along the coast at Juan la Pins.
There is a small museum of photography in Mougins. It's so so. However the Museum of Classical Antiquities in Mougins is superb. Well worth a trip.
I think Renoir's house and museum in Cagnes is closed for renovation. If you are in Cagnes sur Mer, head up the old town (Haut Cagnes). Walk or take the free bus from the main bus terminal. Near the church is a great restaurant - La Goutte d'Eau. It's not expensive and the food is simple home cooked fair, but delicious. Say hello to Fabrice from me.
In the other direction from Nice, with a spectacular drive along the grand corniches, you have Menton. Jean Cocteau museum worth a visit. Inland from there is a short windy drive up the moutains to St Agnes. Village in a spectacular moutain setting. There is a Maginot Bunker you can visit there too (google for opening times as closes for lunch etc.).
Plenty more places to see and visit. If there is anything you are interested in ask away or feel free to pm me. I have visited that area a lot in the last 10yrs and have driven all around the region.