If you can make it into the city, Pizano's has a decent thin crust, but Pat's Pizza has a better representation of Chicago thin crust in my opinion. If you don't mind killing a lot of time, Great Lake has some phenomenal pizza but I'm not sure they're open anymore. (Their hours are only evening, and they're kind of open when they want to be). But if Vito and Nick's is too far north, you'll likely not make it into the city. (Btw, there's a Vito and Nick's in Tinley which should be close to you. I don't know how it compares to the VN in the city, but it's supposed to be the same owners, and it was respectable pizza when my wife and I tried it.)
If you've never had deep dish, I highly suggest getting some Lou Malnatis, some of my favorite Chicago deep dish. Even though they're a chain, they're remarkably consistent across them, so any Lou's should do.
Spacca Napoli is probably the clear winner in terms of Neapolitan style in the city, and worth checking out if you like that style. Also in the city, so might have to cut that out.
Some other great things to try in Chicago:
Italian beef at Portillos. (chain) Get it dipped, and either with sweet or hot peppers... hot if you like spice.
Depending on how you got into Chicago, there's a restaurant called Birriria Zaragoza near Midway that has phenomenal food... they roast goat, make their own clean vegetable consomme, make their tacos from scratch... it's literally some of the best taco's I've had. I don't typically like goat, but the way they cook it, it's phenomenal. Great salsa, great meat, great consomme, great tacos.
Also, Garrett's Popcorn makes some great caramel/cheese popcorn... there's something about their combination specifically that is ridiculously addictive... most folks I know that don't even like popcorn can't stop eating it... it's literally like they put crack in it.
Calument fisheries is slightly north of you, which has some great smelt... but their winner in my book is the cold smoked shrimp. Seriously plump, delicious, and smokey... I could eat a few lbs of that no problem.