+Biot (Glass Manufactory)
+Cannes
+Monte Carlo (Don't bother with the high-end part of it, head for the old centre with the palace, the narrow streets. It's surprisingly affordable there) I've been there once. It's was nice, nothing less, nothing more.
+Nice is worth a trip.

If you want to go the extra mile
+ Porquerolles (An Island south of Hyères): White sand, clear water, nice diving spots
+ Saint-Tropez (Mrs_Dragon might like to get Rondini sandals). A few miles south of Saint-Tropez, you can eat excellent Bouillabaisse on a private-ish beach (Chez Camille - Rammatuelle). If you happen to be in that corner anyway, Cogolin (not to be confused with the horrible Port Cogolin) is quite nice as well.

These are a few places I remember off the top of my head. There might be a few places more to the West.

Your planing should have take into account, that

• Many towns are dead once the summer season is over. Places like Nice or Saint-Tropez are, for that matter safe havens, as they rely less on seasonal tourism. In the shoulder seasons, Saint-Tropez is actually very, very nice: No mass tourism. No wannabes making a fuss. Just a little, calm town.
  Places like Saint-Maxime (on the other Side of the gulf of Saint-Tropez) die out, as the French (that spent their summer months there) leave their appartements for the winter and head back to work/school.
• I think that the Côte d'azur is very depressing in bad weather. The azure water turns grayish. Terrasses are empty. Only a few people are outside. You might take that into consideration as October can be very pleasant or very very wet. A few years back the rainfalls were that heavy, that driving on the motorway, I felt like navigating a boat instead of driving a car.

Furthermore, as some mentioned before, Nice has like any large french city bad neighborhoods. I wouldn't go as far and claim, that it is as bad as certain parts of Marseille, Lyon or Paris, but such places exist in Nice as well. Follow the signs and the instructions of your navigation system/app and you'll probably end up fine.