New Orleans itself has an extensive historic streetcar network that runs along the riverside, and through the down town area. This is well supplemented by a straightforward bus network for which you can but all day passes. With New Orleans reputation as a hard partying town, getting back to your hotel in the evening can be done in a taxi, although when the bars finally start to close, it can be difficult to find a cab.
Renting a car in New Orleans is a great idea if you want to explore the surrounding areas, and good value car hire is available, particularly if you book prior to travel.