Villefranche Sur Mer is so incredibly beautiful. You must visit here. Consider staying here too.

If you do stay in Nice, the LeMeridien is nice. Last June I got a 100 EUR rate from the LeMeridien website. I could not believe the rate!! The hotel has a 'plage privat' (private beach) area with its own beach chairs, towel service, etc. Save your 15 EUR for this service, and lay your own towel down on the beach - for free.

I have also stayed at the Boscolo Plaza hotel. The Boscolo hotel chain has a few hotels in Nice.

There is also a public bus that travels between Nice and Monaco. I forget the bus number, but the bus is labeled "Monaco/Menton". Just hop on the bus at the Nice central bus station (a few minutes walk from the Galeries Lafayette store), and hop off wherever you feel like -- Villefranche Sur Mer, Eze Sur Mer, Monaco, etc.

Enjoy!