If just pizza:
Piece - New Haven style pizza.
Spacca Napoli - Neapolitan, and nearly identical to what you can get in Naples in terms of quality. (If Jonathan is there, tell him Derrick, the Asian guy partnering with Paulie Gee sent you).
Coalfire - Americanized Neapolitan, but done quite well.
Lou Malnati's - Deep Dish Chicago
Vito and Nicks - Thin crust Chicago sausage pizza
If you have time for more, let me know... the list is long, but these are the key players in Chicago, IMHO.