re: Lunch with the kids in NOLA today.

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Around the aquarium, within walking distance, both kids under 5.

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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.