We stayed in Nice for 4 weeks last august with dd's 13 & 3 and ds 10. (and will be again this summer but only with ds and dd2, dd1 staying at her nan's).
Beaches - The beach in nice is pebbles, for sandy beaches catch the train/bus to Antibes or Villefrance.
Air conditioning - we didn't have any but a fan was provided which came in useful.
Our accommodation was in Vieux Nice, which was really nice. we all enjoyed walking from our accommodation to the promenade, never tired of the narrow streets even when they were busy.
We're staying in Vieux Nice again this year but different accommodation.
Places to visit - Marineland at Biot (nr Antibes), Aquarium at Monaco, Beach at Antibes, Museum of Modern & Contemporary Art in Nice (my dc's enjoyed it).
This year we're looking forward to trying out the trams, trip to Ventimiglia for the market, Aqualand at Frejus and everything we did last year.