Nice is 15km east and 15 minutes by train — the old town, the Promenade des Anglais, the Matisse Museum, and the Chagall Museum are all within reach of a half-day.
Antibes is 10km west and 10 minutes by train. The Picasso Museum, housed in the château where Picasso worked in 1946, and the old town within its ramparts make this the most rewarding town between Cagnes and Cannes.
Saint-Paul-de-Vence is 8km north, easily reached by bus. One of the most beautiful hilltop villages in Provence and home to the Fondation Maeght, one of the great modern art collections in France. Busy in summer but justifiably so.
Vence is 10km north and accessible by bus. The town itself is pleasant; the reason to go is the Chapelle du Rosaire, decorated by Matisse between 1948 and 1951 — his last major work, and one of the most serene rooms in France.