I went to college in NOLA and lived there for 6 years. No one above has steered you wrong. I'd especially second Cochon Butcher. For me, that's a must. Green Goddess in the Quarter is one of the best new restaurants. Its a little hidden on a pedestrian alley - but its awesome. Whenever I had out of towners in, I took them to Court of Two Sisters for brunch because I think its a great way to sample a lot of different New Orleans and Creole flavors and dishes. Its also something of an insitution, usually has jazz playing and is just a really good meal. Champagne Brunch at The Columns on St. Charles Avenue is a great, somewhat upscale way to start a Sunday. Even if you don't have a destination in mind, spend an hour or two riding the St. Charles streetcar. You'll really see some different parts of the city - incredibly different from the Quarter. You'll see the universities and all the gorgeous mansions along St. Charles. It may be too late for this, but you know if you stayed Friday and Saturday that you'd get to experience some early Mardi Gras parades, right? Parades are so much fun and, to me, the entire point of MG. I promise its not the drunken madness you have in your head and because its so early in parade season, its all about the locals. If there's anyway to cheaply and easily change your plans, I'd absolutely stay Friday and go see the 2 Orleans Parish parades that day/night.