I'm from Louisiana, so clearly my favorites will be near here.
Restaurant August in the Warehouse District of New Orleans could be the single greatest dining experience I've ever had. We went not long after the finale of Next Iron Chef (in which Besh was robbed, but that's another topic) and had the smoked swordfish sashimi that he made in the finale as part of a tasting menu. Outstanding food, wonderful restaurant, great service. Can't say enough about this place.
Another great Besh restaurant, and one that I go to much more frequently, is Luke in New Orleans. Four words: cochon de lait sandwich. Plus the beers they have brewed for them are great.
There are too many other restaurants I love in New Orleans and Baton Rouge to name them all, but a few that I'm particularly fond of are: Bayona, Galatoire's, Felix's, The Gumbo Shoppe, Juban's,
Outside of New Orleans, there's small Italian place called Da Leo Trattoria on South Beach. Food is good, but the atmosphere is better. Probably the best lobster ravioli I've had.
Paesano's in San Antonio is a nice place. For me, the best dish is the Frutti di Mare. Love it.
Another old favorite is the Snake River Grill in Jackson, Wyoming. Lot's of great game dishes, especially the rabbit and the elk.
Slightly off the grid is BO's Fish Wagon in Key West. Basically a parked food truck with a few tables under a shanty roof, but the best fried grouper sandwiches.
TM