There are plenty of places nearby with really good food. You are right at the foot of Poydras St. where it meets the river and there are a bunch of great places within walking distance. Mother's serves po-boys and traditonal Louisiana food just two blocks down Poydras from your hotel. Also, in the wharehouse area, check out Rock n' Saki for excellent Japanese food and sushi, Rio Mar for seafood with a latin kick to it, Liborio for excellent Cuban food and fast service, and Riche, the new Todd English restaurant attached to the casino.
For higher end food within walking distance, you have 7 on Fulton St. almost across the street from the Hilton and a place called Cafe Adelaide at the Lowes Hotel on Poydras St. close to the Hilton.