We are going to New Orleans at the end of August this year with our four kids ages 14, 13, 12, and 8. This will be their second trip and our third. The Embassy Suites on Julia St is a great deal for families, you can book a room for about $100 a night for your whole family. Check hotels.com. The rooms have a seperate bedroom so you can have some room to spread out. A full breakfast buffet is included each morning so that can really help with the food budget. For two hours each evening they have free drinks for adults. This will be our third stay there and will stay here each visit. It is in a very centrally located part of the city. If you are driving parking is $30 a night but that seems to be the going rate everywhere.
We are going to buy a membership to the zoo and aquarium for $135 this will save us a little bit of money and we will be able to get into both places, you also get a discount for the IMAX and insectarium. Our kids loved cafe du monde but will not do the muffelata sandwich again, too bad cause it is so cheap! The kids also liked eating at Jimmy Buffet's Margaritaville, so we will take them there again.
I would be interested in hearing about any more budget ideas, thanks OP for starting this thread.