Well, if you are down for cabbing all over the city and potentially suburbs, tell me what you wanna eat and what kind of experience you are expecting.
If you want some of the best fried chicken ever, go to a Harolds in a bad neighborhood. Call your order in advance, chicken is cooked to order and takes like 15 minutes and you probably don't want to hang around and wait for 15 minutes if you aren't from around there or think you know better.
If you want really good Italian that won't break teh bank and I'm talking REALLY GOOD, go to Calo in Andersonville. Chicago cops and gangsters can be found eating there during the same hours. Gnocci Gorgonzola is my favorite there.
Find a Lou Malnati's for pizza if you want a pan pizza. It's always decent. If you want to go to Uptown, you can get some awesome NY style thin crust pie cut pizza on the cheap like it should be - Gigio's.
Saloon Steakhouse downtown is a very hidden gem last time I was there. Awesome grassfed steaks 45-70 bucks. Classic steakhouse, fantastic service, dark leathery and warm atmosphere, won't break the bank and be sterile like a lot of chicago steakhouse restaurants.
Also, if you are going to be around for some tourism, just go down to Chinatown. Eat at a busy restaurant. Lots of good times down there.