Let me just say that if you want to, DEFINITELY go see New Orleans.
Its not Mardi Gras, but oh well, it'll still be a party. Bourbon Street is the party place. Fell in love with the city, so much so that I want to have a Jazz funeral when I die.
Bring some really nice clothes if you want to check out some of the more famous restaurants (Antoine's, Brennan's, Commander's Palace, etc.) Jacket and tie for supper.
Have the Crawfish (also called mudbugs). And definitely, if you can afford the restaurant, have Banana's Foster at Brennan's. Its to die for.

Best to do alot of research about where you want to go, in four weeks you will probably only get to do a quarter of the country if you're driving. And that would be pushing it.
If you wanted to stick to the south, or try going up the eastern seaboard, that's probably all you could get to. Just do a LOT of research.