A lot will depend on your style of travelling. The French Riviera is fantastic, but the BIG difference, when comparing it with the other cities you are thinking of visiting, is that here you are going to need a rental car, IMO, because what really makes the place so outstanding are the long, scenic, and very slow drives* along the coast, between St. Raphael and Montecarlo, with stops in Cannes, Antibes, and Montecarlo. Nice itself is ok, but pales in comparison to the rest, and feels like "just a city" after visiting Cannes. The corniche routes between Nice and Montecarlo are out of this world, but you will need time, and wheels. Public transport exists, of course, but you will feel like murdering the driver for not stopping at the 'right' places. Shopping in Antibes, in particular, will make your VISA card smoke.

*Edited to add: don't even think of taking the freeway; drive along the 'bord de la mer' all the way, and allow at least one full day, just for the drive (stops are extra).