Around the aquarium, within walking distance, both kids under 5.
Kids under five, by Aquarium I would say.
(well depends on price point)
Palace Cafe is right there and is not really expensive and good at accommodating kids and will offer a good NOLA menu.
New Orleans Hamburger and Seafood is good for a quick lunch.
especially with kids.
You could take the streetcar or walk the riverfront and go to the places closer to the French Market. A lot of choices there that are family friendly also kids like the area seeing boats, and streetcars pass.
I would say walk around and look at menus in that area and step into a place that has a dish you would all want.