Just to clarify, I think the cemetery referred to above is actually the so-called Castle Rock, with classical ruins on the top. The Nice cemetery is actually up in the Cimiez area, by the city rose gardens and the Franciscan monastery. Both Matisse and Chagall are buried in the cemetery, and it's a beautiful place to visit.

Not Chagall: Dufy. Sorry.

Wow! Thanks for the exchanges everyone. All the information is valuable. We immensely enjoyed Josephine Baker's castle/home in the Dordogne region of France so we would the villa recommendations in Nice too.

Antibes is a must! Such a beautiful place and well worth going to.
Day trip to Cannes is quite interesting but doesn't have to be a priority.
If you go in the middle of the year, around july is the Nice jazz festival which is a lot of fun. Just FYI

Thank you everyone. We had a fabulous time and did from Menton to Cannes.