A couple of other places you might want to search here that are in easy walking distance of the Hilton: Cafecito (Cuban lunch), Chicago Curry House (Indian), Custom House (a bit higher-end, a lot of changes in the kitchen lately), Rhapsody (also slightly higher-end but a favorite of mine with its new emphasis on Italian), Hackney's (hamburgers, beer, and the like).
Strongly second Jazz Showcase and Buddy Guy's and BG's does have a decent Cajun/Southern menu. Lou Malnatti's (on State) for deep-dish pizza, Edwardo's (on Dearborn) for stuffed pizza, but you'd have to cab it to get the best Italian beef in the general area (and across the street--Italian ice at Mario's) at Al's #1 on Taylor (roughly 2+ miles away). There's a Portillo's somewhat closer, but Al's is an experience.
"The fork with two prongs is in use in northern Europe. In England, they’re armed with a steel trident, a fork with three prongs. In France we have a fork with four prongs; it’s the height of civilization." Eugene Briffault (1846)