Original house of pancakes (Rush and Walnut(?)). Best breakfast food in the city. Get any omelet, or...shit, everything is good. Bring your biggest appetite, and go early, or expect a line.
Five Faces (Division and Dearborn). Tiny hole-in-the-wall gyro place. The menu is enormous. Don't order anything but gyros and sides. It's almost blasphemous to order a burger/tacos/etc. Super-greasy, and amazing.
I'll think of a lot more, but every trip to Chicago should involve those two, at least.