There's Ponton in the Old Port across from the Centaur. They're the oldest costume shop on town and have a large inventory of costumes for rent (3 floors!!!) as well as to sell, although after the phone conversation I had recently with one of their sales reps, I'm not too impressed with their customer service. It went something like this:
Me: Hi! Do you have the Mad Hatter's hat from Tim Burton's Alice in Wonderland?
Salesgirl: Well, I have something similar.
Me: I'm looking for the licensed version, the one from the film.
Salesgirl: Well... (pause with barely audible huff of impatience) That particular one would be in California somewhere.
Me: O_o... *click*
I'm going to assume she was new