I will be staying in Nice for 3 nights in late May and won't have a car. I want to go to Vence, St. Paul de Vence, Eze, Cap Ferat and Monaco (Monte Carlo) while I am there. I know there is bus and tram service in the area but am not sure which ones will get me to the right places. I tried going to SCNF but could not glean any information as to how to get about in this area. Does anyone have any advice?
I was in Nice last summer for two nights (should have stayed longer) without a car and managed Vence and S.t Paul de Vence by bus. The local TI office or your hotel should be able to give you directions. Both Vence and St. Paul de Vence are uphill, so the tram won't go there, but one bus takes you to both places. It's a short train ride to Monaco from Nice Ville station. Sorry can't help with Cap Ferat.
The French bureaucracy supports many official tourism offices, both municipal and regional. Google should turn some up, and as you study possible destinations, you probably will find more on-line offices to help. The regional trains, not TGV, have local stops and perhaps easier views of the sea, although the TGV high-speed trains can't go so fast along the coast either. Always for rail questions, consult www.seat61.com
Rick Steves' guidebooks for either France or for Provence and the French Riviera summarize train and bus connections to each destination you listed. If you don't need the rest of France, then the more focused book is the one to take with you. See more bus info at www.lignesdazur.com and confirm schedules locally when you're there. Bus schedules are much reduced on Sundays.
Getting to the towns along the Riviera from Nice by rail is very easy and inexpensive . The train from Gare Nice - Ville will take you to Monaco in about fifteen minutes , about ten to Villefranche . Villefranche is particularly lovely and there is a wonderful coastal path ( Sentier Littoral) that you can walk to Cap Ferrat . The home of many of the 1% , the homes are discreetly hidden by lush foliage ( like much of Newport RI ) and one of the main roads is , like Newport , named Bellevue Avenue . The Village of St. Jean , the lighthouse ( phare ) and particularly the Villa and Gardens of Ephrussi De Rothschild are well worth a day . Get off the train at Villefranche and go early . Back in the Halcyon days between the wars ( for the 1% ) , the English writer , W. Somerset Maugham had a home on Cap Ferrat , and a street is named for him , He once famously ( or infamously ) quipped that Monaco was " a sunny place for shady people " One of his short stories , set in this heavenly area and worth reading , is entitled " Gigolo and Gigolette " . Enjoy it !