Exactly what are you looking for. There is a "local flavor" to the Grill Room at the Windsor Court Hotel. If you opt (not inexpensive, but worth the $), do take in the murals, and ask for a "sheet" on each one.
We also enjoyed 7 on Fulton, just blocks away. While we were there for the food, I will admit that the "bar scene" was very active. Web site: http://www.7onfulton.com/
7 On Fulton
701 Convention Center Blvd, New Orleans, LA 70130
New Orleans Grill
300 Gravier St, New Orleans, LA 70130