Nice is a good place, but the shopping (avenue Jean Medecin is not brilliant).
The old town is nice, but as said the whole place can be a little expensive.
I used to live in Antibes which is lovely - strongly recommended but the beaches get very crowded in August!
http://www.antibes-juanlespins.com/eng/index.h tml
It has an old town surrounded by the old walls, a marina, some great restaurants and a Provencal market.
Antibes is about 30 mins max from Nice. A taxi from Nice would set you back a bit, otherwise you can get the 'Navette' coach shuttle, hire a car or the train would be the best way.
From Antibes you are then about 20 mins from Cannes and can also drive to Mougins, St Paul de Vence all within about 30 mins.