As a born and bred Chicagoan and Buckeye loyalist, I have to weigh in on the pizza and hot dog conversation. All of the typical deep dish places have been mentioned, but if you want to try a pizza with the best ingredients you will find and a medium-type of crust (not a paper thin nor deep dish) then you must try Home Run Inn pizza. There are now half a dozen locations, but the original on 31st street is the place that White Sox fans have frequented both before and after games since the late 1940's.
For hot dogs, I would definitely choose Gene and Jude's in River Grove. Not downtown, but worth the trip. Best french fries you will eat, and they are loaded on the dog and bun when you order. Check them out online if you want more info.
Keep up the great work, and we are looking forward to Eat Too Brutus later this year. Go Bucks!