Surely one of America's Great cities. To see: the French Quarter (you could easily spend an entire day there) and the Garden District. PLEASE note: I would not recommend that you stray outside the boundries of the Quarter; crime (post-Katrina) continues to be a serious problem.
Also, you really should rent a vehicle and make a trip up the River Road (or take I-10 up to Baton Rouge and then transfer on to Highway 61) and explore some of the Antebellum architecture in St Francisville (as well as the town itself). Of note: The Myrtles (just outside St Francisville, heading north), Rosedown, Oakley Plantation and the gardens/ruins at Afton Villa. Enjoy your trip!