I remember New Orleans was the first place I ever tried alligator meat as a kid. I'm sure the kids would enjoy beignets at Café du Monde. Also maybe look for a place with Bananas Fosters. Get some crawfish and gumbo for the kids too. Ride the streetcar trolleys as Rosalie mentioned, that's fun to do. You could go see real gators on a swamp tour. Check out jazz at Preservation Hall which should be all ages. Go to City Park and check out StoryLand. There is also the Louisiana Children's Museum. If you happen to be driving to New Orleans, I remember being amazed as a kid by the Lake Pontchartrain Causeway, the longest continuous bridge over water in the world.
I went to NOLA when I was 12 and my sister was 10 (in 1950). My father was attending a conference. Things have changed a bit since then of course. I remember taking a carriage ride and going to Antoines and the Three Sister's restaurants. More recently when I went I found that NOLA has a nice zoo and an aquarium. We also rode the trolleys all around town. There is a great WWII museum. And we took the paddlewheel steamer down to Chalmette where the ranger gives a great talk about the Battle of New Orleans (he doesn't sing the song, but there's a good song to go with it). We were there in December so there were concerts in the cathedral. We went to the markets and saw Joanie on a Pony and ate beignets.