Our favorites (my kids are 5 and 4):
aquarium, then ride the Algiers ferry back and forth across the river afterwards (ferry is free to pedestrians and the entrance is right by the aquarium)
zoo
play at City Park, just explore, play on playgrounds, or go to Storyland, an adorable little park with a Fairy Tale and Nursery Rhyme theme. Storyland is $3/person
walk around the Quarter, eat beignets, listen to street musicians, walk through the Blue Dog gallery
our children's museum is pretty good, and getting better! They've been renovating
ride a street car!
I'm sure I could come up with more, but that'll get you started!