Montpellier is a compact city and walking across the whole city center does not take long.
By bike
The tourist information office have a map Montpellier à vélo, which shows you where the best places to go by bike are and places where it is dangerous to cycle. The city has an extensive network of cycle paths, often separated from traffic for added safety. There is also a bike path running all the way to the beaches at Palavas-les-Flots and Carnon. The ride from the city to the beach takes about an hour.
Bikes may be rented at machines VéloMagg (http://www.velomagg.com/10003.html) in various places in the city centre including Virgin, the tourist office on the place de la comedie and the main TAM velo office, located adjacent to the train station. The price is 2⬠for one day.Just remember, if you are cycling in the old centre, that there are streets which are actually staircases and although they are a sight to behold the rue du bras de fer, a glorified shopper bike will not tackle them as well as a fully suspended Cannondale.
Be advised that whereas a smart card allows a 24h/day use, only a small subset of the Velo Magg kiosks operate on Sundays, in which case it may be better to visit one of the manned offices, either adjacent to the train station or near l'Opéra.
By car
There are several parking lots in the city centre. However, it is inadvisable to travel in the city centre by car as it gets busy, you will get stuck in traffic, and it's not very well signposted. The city centre is also a traffic-free zone! Your best bet is to park by a tram station at the end of a line such as Odysseum on line 1 or Sabines on line 2, but if you do insist on driving, parking in the Polygone shopping centre will save you a lot of your precious spending money!