Public transportation in Nice and the whole surrounding area is wonderful. I recommend that visitors NOT rent a car; we lived here two years before we decided to rent one and that was because we like to go over to Italy and up into the further villages that are not accessible by PT. But as a visitor, with a couple of weeks to explore, you will not need a car.
You may arrive at the airport or by train. The Nice Cote d'Azur Airport is very easy. There are two terminals with a bus that will take you from one to the other. There is an Airport Bus - I think the fee is around 4 euros - and there are taxis. But for getting into town from the airport, I like to take the #23 bus which you can pick up at Terminal #1 and which costs 1 euro. It will take you to the main train station, passing points near the center of town, towards the west side. If you arrive by train, you can take the same bus to hotels on the west side of town. Or you could just walk to the center of town if that is where your hotel or rental is. There are other buses that can take you to the east side of town and the port area. Your hotel or rental owner can tell you which bus is best for you.
When you board a bus, you will pay one euro for a ticket; you must then "validate" your ticket in the machine behind the driver. There are stiff fines if you are caught without a validated ticket. The ticket is good for a transfer within 74 minutes, and you must validate the ticket on the next bus or tram that you take.
Getting around town:
The bus and tram system is terrific. There are buses that will take you up to the Museum area in Cimiez, to the Port, and anywhere else you will want to go. The new tramway goes all the way down Av. Jean Medecin, our main shopping street, through Place Massena, the center of town, and past Old Town, to beyond the Acropolis, the main theater and convention center of Nice. The bus or the tram is one euro - you will need a ticket for the tram before boarding, available at machines at each stop. Remember to validate after boarding.
To get to the many other beautiful and interesting village that you will want to visit during your stay, there are buses available at the Gare Routiere which is located along the tram line near Place Garibaldi. The #100 bus will take you, for one euro, as far east as Menton on the Italian border; a very popular stop is Monaco/Monte Carlo, about an hour ride from Nice. In the other direction there are various buses for Antibes and Cannes (the same bus), Vence and St. Paul de Vence (the same bus), Grasse, and so forth. Another very popular destination is the perched village of Eze - another bus at the Gare Routiere. Almost all these trips are 1 euro, so you can see that it is better to take the bus rather than renting a car - you will be busy looking at the beautiful scenery along the route.
Besides the city buses, there are two tourist options for Nice itself: a Hop on/Hop off bus and a Tourist Train. The two trips are quite different but, if you want to do only one, I would recommend the less expensive Tourist Train that will take you a bit into Old Town and by the Flower Market and also up to Le Chateau, the hill that separates the main part of Nice from the Port. The views from there are spectacular. However, the Tourist Train runs only in the nicer months while the Hop on/Hop off runs year round.
There are also bus tours of the region through Santa Azur (located on Jean Medecin, west side, just north of Gallerie Lafayette). For instance, this month (April 2009) they offer one day tours to Toulon, Les Arcs Sur Agrens, a medieval fair in St. Maximin, and various other destinations. They don't seem to have a website, but once you are in Nice, just go to their storefront office and pick up a schedule.