I entirely agree with AzurAlive. We recently came back from a trip to Nice. We fell in love with Villefranche-sur-mer. It is about 15 minutes by train to Nice. It is peaceful and gorgeous!
I would also make time to see Eze Village. It is an amazing medieval village. As far as Monaco is concerned, we understand what you mean by a concrete jungle. We were a little disappointed there.
Nice really is a good base, though. It didnt feel like a 'big' city to me. We adored it. We loved to visit the Old Town (Vielle Ville) especially in the morning with the flower market and in the evening for dinner. The streets were quaint and lovely.
Nice is about 20 minutes from Antibes and then to Cannes, if you would like, by train.
Antibes was also very pleasant!
Really you can not go wrong! The trains make places very easy to get to, so wherever you pick, I would think you would be happy!