Wherever you end up staying, don't fail to take the kids to the Aquarium. Tres cool.
They would probably also enjoy beignets at the Cafe du Monde (do not wear black as you will wear powdered sugar for the rest of the day) and the outdoor-ish market, just watching the world go by. Plenty of good cheap junk.
NOLA is kind of a grown-up place for tourists, so I don't have any other really great ideas
Pooh Bear makes a good point. Cruise the net for ideas of what to do.
Our favorite restaurant is Bayona ($$$$$ and not a place kids would like, but you could get a hotel sitter?) They might like Mother's for po'boys or the Acme Oyster House. Brennan's for brunch is a NOLA staple (any day of the week) but if your kids aren't into serious chowing down, that may be a non-starter.
Whatever, cherchez les bon temps et lassiez les bon temps roullier !!!
pamda -- CM First-Time Cruisers Editor and big fan of NOLA