If you do a search on this forum (New Orleans) this topic has been covered quite a bit. You'll find some helpful suggestions in the links posted below. The only place that is closed that I can think of, is Cafe Bamboo.
re: Suzy Wong
Well, for ethnic options in Metairie, you could eat the variety of Indian vegetarian dishes at Taj Mahal, or perhaps the non-meat Lebanese platter at Byblos (baba ganouj, hummus, rice pilaf, falafel, etc.). Or if Uptown, you could go to Taj Mahal's sister restaurant, Nirvana, or the Uptown location of Byblos. Both on Magazine Street. Just a few thoughts...
Bennachin in the Quarter is pretty good. And I haven't yet been to Green Goddess, but it doesn't look like you can go wrong, there. A lot of the more popular restaurants will set you up if you call ahead. These include Bayona, Commander's Palace, and even Cochon, surprisingly enough. Commanders' has a vegetarian option on their standard menu. I heard that Muriel's can put on a good show for the vegetarian, too.
Let's see. I think Meauxbar and Dante's Kitchen have those options on their menus, lunch or dinner or both. I think Iris does, too. Domenica has pizza and a lovely cheap happy hour. I think you can sort of get by at Bourbon House.
Breakfast at Ruby Slipper, Huevos, Stanley, and Surrey's will do the trick.
There's a fried green tomato po boy at Mahoney's (haven't tried it--make sure they don't have the implied shrimp included). I think Parkway has a french fry po boy. Red Fish Grill has a veggie sandwich for lunch. I can't imagine they wouldn't do it for dinner. I think Central Grocery will even make you a vegetarian muffaletta.
Is that enough? How long will you be in town?
930 Tchoupitoulas St., New Orleans, LA 70130
Commander's Palace Restaurant
1403 Washington Ave, New Orleans, LA 70130
430 Dauphine St, New Orleans, LA 70112
736 Dante Street, New Orleans, LA 70118
Red Fish Grill
115 Bourbon St, New Orleans, LA 70130
4408 Banks St, New Orleans, LA
307 Exchange Place, New Orleans, LA 70130
1212 Royal St, New Orleans, LA 70116
144 Bourbon St, New Orleans, LA 70130
Ruby Slipper Cafe
139 S Cortez St, New Orleans, LA 70119
123 Baronne Street, New Orleans, LA 70112