Not sure how large your group is, what type of cuisine you seek or if you have a car but in general the following might be helpful in my opinion:
There are more than a few casual places that would have vegan dishes, looking into it ahead of time is best. Call to be certain of hours, dish etc If you do a search of this forum, you'll come up with suggestions.
Surrey's, Slim Goodie's, both on Magazine St Satsuma Cafe (they have a facebook page with menu) in the Bywater to start....Gumbo Shop has a vegetarian dish, and vegetarian gumo z herbes....
3218 Dauphine Street
New Orleans, LA 70117
Slim Goodies Diner 9-3
3322 Magazine Street
New Orleans, LA 70115-2411
Lebanon Cafe Uptown, Bennachin (african) on Royal St
Vegan Orleans has many suggestions and descriptions, THE LINK:
Surrey's Juice Bar
1418 Magazine St, New Orleans, LA 70130
1500 S Carrollton Ave, New Orleans, LA 70118
1212 Royal St, New Orleans, LA 70116
Dick & Jenny's has always been pretty vegetarian friendly. I feel confident that they would happily accommodate your vegan friend. I would imagine Dante's would too. Just call ahead, of course. I'm sure you're probably aware, but in general the vegan will need to be wary of seemingly innocuous meals like red beans and rice - very rarely is that dish actually vegetarian.