foods to avoid in N.O. in December?
Well, tomatos won't be the great creole variety you'll find in the late spring/early summer. That's the first thing that comes to my mind. Eggplants, artichokes, any other typical summer vegetable. Blue crabs and even the soft-shell versions will be less available, that time of year, although you will still see many soft-shell stuff.
Beside oysters mentioned, other foods that will be "of season" in December include sweet potatos. If you get outside of the french quarter, you may see various Oppalousa Yam Men selling their wares from pick-up trucks. Baked in a pie, is my favorite way to eat them. Another product you will not likely find in resturants, but is worth seeking out are local Louisiana oranges. I believe pompano will also be around. One of the great off-menu treats at Galatouires is the grilled pompano topped with lump crab meat (my favorite entree there after gorging on the appetizers).