http://www.nomenu.com/RestaurantsOpen.html
http://www.offbeat.com/listings/restaurants.php
Lists like these make me so hungry I can't stood it! : http://www.chowhound.com/topics/500188
Some of my picks:
Muffaletta: Central Grocery. Ok, IMHO, they used to be better - didn't everything? The Gendusa bakery for the wonderful bread was taken out by Katrina. Napoleon House also perhaps. Nor Joe Imports in Metairie. For a great introduction to mufflelettas, see here: http://offthebroiler.wordpress.com/2008/01/27/otb-classic-for-the-love-of-the-muffuletta/
Oysters:
Poboys:
Beignets - some places are great, some places the opposite. Best is Cafe Du Monde. Morning Call used to be downtown but relocated to the burbs (Metairie or Metry to some), but also wonderful.
Galatoire's - Dress code. No reservations downstairs, reservations taken for upstairs.
Brigtsen's - NOT downtown - in Riverbend area.
Liuzza's - bonus - draft beer and soft drinks come in 18 oz frozen goblets
Mother's (ok - often overrun by tourists)
Domilise's, Bozo's, Central Grocery,
345 Baronne St.
New Orleans, LA 70112
(504) 525-9678