As Nigel noted, it is a very busy time, so shift your days if possible. If not, just avoid Cannes the day or two afterward as the streets will still be filled with barriers and temporary structures being torn down.
Besides the other destinations mentioned:
Train des Merveilles goes to the border downs in the lower Alps. It is a special departure (AM) from the main Nice station, with the last few cars reserved for the tour (with narration). You go to an end point, like Tende (nice museum of the local rock etchings) and hit another village on the way back like Saorge.
Tourettes-sur-Loup is a great village, just beyond Vence, but just beyond there is Gourdon, a perched (hilltop) village over the Gorge du Loup. This is best done with a car or via small group tour, as the public transit is less regular.
You can take a ferry from Cannes to St. Honorat or Ste Marguerite (also from Nice) or a coastal tour.
Also in Nice, people typically visit Le Chateau (Castle Hill). There is an elevator for free next to the Suisse Hotel or you can do the climb (or walk down, it is a nice walk). Note the Cours Saleya market turns into an antique/flea market on Mondays. There is a Nice museum 15E pass for three days, and you have over 10 to choose from, including Matisse, Massena, MAMAC, etc. (The French Riviera pass is also still being sold)