Nice for 5 nights September 27-Oct.2

First, get a copy of Rick's book on Provence And The French Riviera. This book has lots of information about the Nice region; note that his general France book has MUCH less information.

The book has all the transit details. Basically, along the coast (Cannes to Antibes to Nice to Monaco to Menton), buses and trains are frequent and cheap, and a car is a hindrance. Higher up (places like Eze Village, La Turbie or St. Paul de Vence), there are buses but they are less frequent, and a car can be helpful. There's also a train that goes inland to some less visited areas.

If you're there for 5 days, a 7 day bus pass (good for all buses in the region except Monaco local buses) is only €15; single rides are €1.50, and this pass would allow you to bop around at will.

To add to the above, see my reply on the hotel question. Get the guide, and note that most people day trip to Monaco/Eze (bus and train), St. Paul/Vence (bus), Antibes/Cannes (train), Villefrance sur Mer/Cap Ferrat (train or bus). Further beyond that main list, people hit +Menton and Ventimiglia by train, or the Lerin Islands by train+ferry. There are two mountain train routes with tourist variants: Train des Pignes (Chemin de Fer de Provence to Entrevaux or Digne) and the train des Merveilles (border hill towns like Saorge)

To supplement the response, I would also add that a Carnet of 10 tram/bus rides are 10E. You can also Uber effectively in the city, but not in Monaco (not allowed, only taxis). Street parking is difficult and while there are plenty of garages, you'll find a tram or bus will be most convenient. There is usually a stop just near where you want to be within the city. Always validate your ticket upon boarding.

I'd only rent a car to go inland and to explore places through the countryside, adding some of the less convenient spots as Harold noted. For example, past St. Paul/Vence to Tourettes sur Loup to Gourdon or to get to St. Tropez/Ramatuelle/Wine Touriing. There are major car rentals at the Train Station and near Le Meridien (I use Hertz all the time -- we have no car, but a place in Nice).

We just left Nice this morning. Had a wonderful time. We have a rented car, but used it once in Nice to go to Antibes- Picasso Museum and a swim area with a sandy beach. Other than that we used the buses and Tram. Rick's France book was extremely helpful for finding the Museums we wanted. Took the bus to Eze, about a 20 minute ride. Our hotel was very helpful with logistics as well.

We spent two weeks in Nice doing day trips by bus and train. By bus: Villa Ephrussi and Cap Ferrat, Monaco, Villefranche,, St-Paul de Venice. Train: Antibes. The buses drive along the water, lovely. We were told it was preferable to take a train to Antibes.
Within Nice, trams and buses. We picked up our rental car at Nice airport when leaving Nice for Italy’s Piedmont.