I think kids might enoy Mardi Gras World, where they can see how the floats are made.

Audubon Zoo, the Aquarium, and the D-Day Museum are my first thoughts. Mardi Gras World is also good, as would be a cemetery tour. a Katrina tour, and a cooking demonstration (very entertaining and you get to eat!).

Jackson Square is fun - there are usually musicians, psychics, artists, etc. set up around the square.

A carriage ride is always fun - you pick those up at Jackson Square.

Preservation Hall is a good place to take kids to hear music - they don't serve any refreshments, so no age limit. There are restaurants and places with music too that aren't bars, so the kids could go - I think Cafe Beneit has jazz outside.

You might want to do a historic house tour - the kids might be interested to see how people used to live. The 1850 House on Jackson Square is a self-guided tour, so you can go as slow or as fast as you like. The Herman-Grimma house an interesting kitchen set up. I haven't seen the rest of the house, so I don't know how good the tour is, but it is definitely neat to see how people used to cook.

Cafe Du Monde

Acme Oyster House, Central Grocery, Tujague's to eat.

One of the Voodoo tours/houses?

If you walk down Bourbon Street at night, they will get to see plenty of [almost] naked women.

Agree with Acme Oyster House, it is reasonable in price and the food is very good! Be prepared to wait in line however, it is always busy.
Also agree with Cafe DuMonde for Beignets! Delicious! The line in the back is for take out. Just enter the Cafe from any side and find a table. We found this out after waiting in line when we wanted to eat our beignets there.

I think walking down Bourbon Street early evening would be fine for your kids(before it gets too drunken) After they close the street to traffic (I think around 6pm) it's fun to walk the street and listen to lots of music from people who set up on the streets.

Agree with aquarium and zoo. Also suggest walking up to the riverwalk to see the river. Maybe ride the streetcar and eat at Mandina's, Juan's, Brocato's or any of the many restaurants at the Canal and Carrollton area. At that age I would also try and do some kind of ghost or cemetary tour.