If the crowds and excitement are starting to get you down you may want to get out and about and visit the small towns and villages outside of Cannes. Alternatively, walk the short distance from the La Crossiette to rue Republique where Place Comdt Maria is one of the town's best-kept secrets. 

Around Cannes are a number of medieval perched villages, including Mougins (about 10 minutes from Cannes once you get up to the autoroute), St-Paul-de-Vence , and Vence . If you want something spectacular, head up to the very perched village of Gourdon, high in the mountains; there's a fine castle to see and fantastic views. If you go to Grasse , make it during the day so you can visit the perfume museum, which has a terrific collection of ancient perfume bottles.
Eze-Village and La Turbie between Nice and Monaco are quite nice to see. Market day in Ventimiglia and San Remo , Italy are something to see. You could go on Friday morning to the Ventimiglia market then stop by Monaco on your way back, then return to Cannes for dinner. You have plenty of time in an afternoon to see Monaco.
Nice has many historic sights, including Roman ruins.   Check out a guide to the Côte d'Azur for some suggested itineraries.

** Note:  The original information for this thread came from the following forum thread: