I'll second the warning about objectionable happenings in front of kids. We went there at the very beginning of Mardi Gras the year of Katrina, so it was a while back. My DH had a conference, and we brought our then 5 year old daughter, other children were there as well. Although we loved it and will go back again, I do want to caution you that while walking around the French Quarter we saw our share of things I would rather my daughter not have seen. This may or may not be true for young teenagers, as well. The partying was pretty extreme--we saw people with vomit all over their clothes being dragged away by friends who were nearly as drunk...but that aside, some of the shops had a lot of questionable items in the windows (think unmentionable body parts of both men and women) on necklaces, as stuffed toys, very risque and obscene sayings on shirts and aprons. Some guy offered me beads to lift my shirt while I was walking to dinner one night. I was holding my daughter's hand at the time and when I lifted it up to show I had a child with me he apologized. We all kind of laughed, but I remember it as a really anything goes kind of place. I think that New Orleans should have the "Whatever happens in New Orleans, stays in New Orleans ..." slogan more than Vegas (where we brought my then 6 year old DD the following year)!
Don't get me wrong, we did a lot of the family stuff mentioned by PPs, and we had a great time, but I just wanted to mention the other stuff so you aren't surprised.