I love the bread pudding at Commander's Palace. It is my absolute favorite. For dessert, try Angelo Brocato's, Sucre, or Creole Creamery. I will say that a lot of restaurants have wonderful dessert menus but you could use these suggestions as an afternoon treat.
The flan at Rio Mar is, without question, the best flan I've ever had in my life, and I'm a flan fanatic. I also like the bread pudding at Bon Ton (but am old-fashioned enough to wish the whiskey sauce were stronger, not weaker!).