There is a lot more to New Orleans than Bourbon St ... waste of time! However just walking around the Quarter is great! Jackson Square, the Riverwalk, the Cabildo, the Aquarium, Harrahs Casino, or the cemetery tours, the plantation tours, ride the street car up & down St Charles Ave, see the beautiful houses and neighborhoods along the way. (there is still lots of rebuilding going on because of Katrina but it's all good
) take a swamp tour, visit an alligator farm.
Don't just look at the ship's tours. Depending on what time of year you will be here determines what festival is going on. There is almost always some kind of festival
Here's a link that can be helpful
I just saw you will be here in December ... add Christmas In The Oaks to the list of things to do while in New Orleans