The downtown area, where most of the interesting sites are concentrated, is compact enough to be explored on foot very easily; in fact many of the prettier streets are pedestrian. You can pick up maps at the tourist office in the Donjon, on square Charles de Gaulle behind the Capitole.
Alternatively, you can rent a fat-tire public bicycle from one of the many “VeloToulouse” stations, for €1/hour, using your credit card, and drop it off at any other station. There are not many bike paths in the center, but one that makes for a lovely ride is the one along the canal du Midi. See www.velo.toulouse.fr for more information.
The public transport system, bus and metro, is well developed from center to suburb but less convenient to get from suburb to suburb, should the need arise. However you are more likely to use it within the center. Most buses run from the cours Dillon, on the left bank of the Garonne, or down the boulevard de Strasbourg. There are two metro lines, line A, which runs sort of east-west from Balma to Basso Cambo via the Capitole, line B, which runs north-south from Borderouge to Ramonville. A single bus or subway ticket cost €1.40, a two-day unlimited travel pass cost €7. For more maps and routes, see www.tisseo.fr.