Stop at the Visitors Center in the French Quarter and get info on walking tours. We took a tour through the Garden District. Our guide was an entertaining young woman who shared lots of information on the history of the homes we strolled past, including some of the famous people who live in them (Anne Rice). She suggested we also take the walking tour of the Louis Armstrong Cemetery and related houses. This turned out to be a great history lesson on the city of New Orleans. For both tours, make sure you are prepared to walk. Take a bottle of water and some kind of protection from the sun.
We took a bayou tour to see alligators and I suggest you skip that and see them at the zoo instead. The best way to get around in NOLA is to get a three-day pass to ride the streetcar and train. Make sure you stroll along the river and do go to Mardi Gras world. It is a fascinating tour of the Mardi Gras floats and you can watch them being built and it's a walking tour.