You will get the most of your money if you rent an apartment in Nice. It's a wonderful city with plenty to do: bars, restaurants, discos, museums, casinos, etc! I would look for something in Vieux (Old) Nice or around the port.
Besides Nice, I personally would recommend in order:
Antibes (large British expat community here)
All of these are FANTASTIC coastal French towns and literally sit on the Mediterranean. They are all small (and as a result, offer nowhere near the amount of things to do as Nice), but are full of culture and are located between Monaco and Cannes; short drive if you want to get out and explore those places. There will be a lot of through-traffic for the millions of tourists going to Monaco, Nice, and Cannes, but the towns themselves shouldn't be too crowded.
Another great place, although not on the coast, is St. Paul-de-Vence. It's a wonderful town and fantastic wine/champagne-tasting venues, in addition to one of the most historic and popular (but pricey) restaurants on the Riviera, La Colombe d'Or (go check out their reviews on TripAdvisor; I wrote one myself)!
Bon courage! Hope this helps!
Lived in Monaco for 3 years! :)