For Barbecue, you might try the Big Thunder Ranch Barbecue and Roundup. All you can eat, Ribs, Sausage(dinner only), chicken, cole slaw, beans, corn wheels(dinner only), which is corn on the cob sliced into wheels, and corn bread. I've eaten there 28 times since it openned April 2, and I'm looking forward to number 29.
The only seafood I have liked inside the park is the Salmon at the French Market in New Orleans Square.
I can't comment on the any restaurants within walking distance, since I haven't eaten at any of them in years.