The best time to visit Nice is April-October, although August can be too hot, humid and overcrowded. Winters are generally moderate, but it's really too cold for swimming or lying on the beach.
There's a world of difference between visiting Nice during high season (late spring, summer, early fall) and low. If you're interested in the sights or spas—as opposed to lying on the beach—go during low season. There are no crowds, hotel rates drop, and it's easy to get reservations in good restaurants. The only downside is that a few of the attractions may have shorter hours.