My wife and I spent our honeymoon in New Orleans. The best decision we made was to stay far from the French Quarter and at The Chimes. Jill, (the proprietor), and her family run a simply fabulous B&B.
Our room was more than big enough for two, with one entrance leading directly to the street (so you don't have to worry about sneaking home late after a few too many drinks, which tends to happen in New Orleans) and another entrance to the breezy, central courtyard. The bed was soft, the water hot and the furnishings clean. Each of the six rooms at The Chimes is apparently decorated in a different style: ours had a relaxing Zen feel.
The served breakfast was generous without being overly filling: plenty of fruit and cheese. Jill and her family are truly a part of the experience of staying at The Chimes: incredibly informed about the city, but happy to listen to your own adventures. (Oddly enough, the other guests we met during our stay were equally fascinating, too.) We were even lucky enough to have Java, the household cat, nap with us one afternoon.
The Chimes is expensive, but I don't think it's overpriced. Sometimes you really can get what you pay for. If you go to New Orleans to relax, stay outside the Quarter. And if you stay outside the Quarter, stay at The Chimes.