You are right to associate New Orleans with rich food that is emotionally and spiritually nourishing but perhaps not that physically healthy.
But there are a whole bunch of New Orleans restaurants that are healthy on all three levels. They include:
Green Goddess: This tiny place just opened May 2009 in the French Quarter and is a hit with local vegetarians. (307 Exchange Avenue, The menu is described as globe-trotting and includes Sweet Potato Biscuits with Pepper Jelly, the Green Goddess Wedge Salad, and Abado Mess 'o Greens Cuban Sandwich. Lots of meat dishes too. Download lunch menu and dinner menu. (307 Exchange Place, 504-301-3347)
Fair Grinds Coffeehouse: A hip coffee place off Esplanade Avenue in Mid-City, not too far from the New Orleans Museum of Art and City Park. At Fair Grinds, efforts are made to serve organic and fair-traded foods and coffees. My favorite is a little bowl of chickpeas with raisins and spices that you can eat hot or cold. The environment is wholesome as well, with Scrabble games on Mondays, yoga upstairs and all sorts of art and music events. See Vegan News (3133 Ponce De Leon, 504-913-9073)
Bennachin: A West African restaurant in the French Quarter, Bennachin serves plenty of meat, but you can find very delectable vegetarian dishes, wilted spinach, fried plantains and exciting ginger drinks.Very casual. (1212 Royal St., 504-522-1230)