I was lucky enough to be taken on a trip (albeit hockey focused) to Chicago in February, hasten to add the Blackhawk's games were really entertaining, the food was even more exciting.
I had read and seen videos raving about The Chicago Diner, and it didn't disappoint, even now my veggie boyfriend says the vegan milkshake (chocolate chip cookie dough with peanut butter, nom nom) is the best milkshake ever, full stop!
The food is amazing too! We went there three times in the week we stayed in Chicago, which kinda says it all. The foods really well prices, especially with the conversion from Pounds to Dollars, a hugely filling 3 course meal for two with muffins to take away would only come to about $50, we always walked away stuffed!