Formal Dining in New Orleans

I'm Looking for a nice formal/romantic restaurant in New Orleans. I searched for a topic on this board but didn't find anything pertaining to a formal place. Anyway, I moved away from Louisiana after college and I'm bringing the GF down to visit friends and family. We are going to spend some time in NOLA and want to have a formal night. I'm looking for a restaurant with good food and a place where we wouldn't feel over dressed (A suit and tie for me and cocktail/evening dress for her)and price is no issue. We are staying at the Sonesta so if at all possible anywhere near Bourbon and within walking distance would be fantastic. Thanks for the help!