Nice is probably your best base, since it is centrally located along the Cote. I can't speak definitively about transportation from Nice to any other locations along the Cote, since I had a car. I do know there are bus routes from Nice to adjoining towns.

Nice is a big city, and an interesting one, worth exploring for a day or two. But you will probably want to spend time on a beach, and Nice's beach is dreadful. All rocks, no sand. However, I can't tell you where the best beach is near Nice, since the only one I'm familiar on the Riviera is in St. Tropez, an hour to 90 minute drive drive from Nice. (If you can get to St. Tropez, which is also worth visiting, go to Pampalonne beach, which is terrific.)

I've been to Monaco once for a few hours and found it very interesting. Whether it's worth staying the night, I'm not sure. I do reckon it will be very expensive.

St. Paul de Vence is definitely worth the trip. It is a lovely walled town, albeit a bit touristy. The Maeght Foundation art museum outside St. Paul is also well worth the trip.

I cannot recommend a hotel because during my two trips to the Riviera I've only stayed in villas (one rented, one a friend's -- lucky me!). There are lots of villas to rent in the area, though they are usually rented for a minimum of a week (and they may be hard to get to without a car).

I hope this helps a little.

Evan in DC