Gino's, Malnati's, and Uno's
Also, I need a good Italian Beef recommendation.
So you're visiting the holy trinity of Deep Dish:
The father (Pizzeria Uno / Due - yes they serve the same pizza at both original locations)
The Son (Lou Malnati's)
and the Holy Taxicab! (Gino's East was founded by cabbies).
Sounds like you're likely going to be mostly downtown, so Al's Italian Beef
(Lasalle and Ontario, just east of Gino's) is a good choice for Italian Beef. I just had one last week!
I'd also recommend Portillo's
(Clark and Ontario). They are a chicago fast-food mecca that serves hot dogs, italian beef, and everything in between. Plus they have beer! And they also serve a mean chocolate cake if you're in to that sort of thing.
And if you're visiting long enough... go to Pequod's
(Clybourn and Webster). It's not traditional deep dish, but the caramelized cheese on the outside of the pan pizzas (don't get thin crust there) is worth the visit.
And I know you didn't mention it, but if you're looking for burgers, there's a lot great places too.
Downtown, a little bit east of the Deep Dish restaurants, the Rosebud
restaurant serves an amazing burger(on Rush and Superior, across the street from Giordano's, a good example of Stuffed pizza, get garlic and spinach).
A bit northwest of the downtown area...Kuma's Corner
on Belmont (at Franscisco) has similar top-notch burgers in many tasty varieties named after Rock and Metal bands (my favorite is the Led Zeppelin, which has cheese, bacon and PULLED PORK!), but the wait to get a seat can be very long (up to 2 hours).
Across the street from Kuma's is a place called Square Bar. They usually serve booze to the overflow crowd waiting for a table at kuma's, but if you stay to eat at Square Bar, you'll be pleasantly surprised that they have some great burgers too!
For thin-crust pizza, there's a ton of places. D'agostino's
has a few locations that serve a good example of chicago thin crust. My personal favorite is Barnaby's, but those are out in the burbs. I also agree, Rosati's
is pretty good thin crust.
If you're looking for one more worthy deep dish, try Pizano'
s (run by one of the other Malnati brothers). They have great deep dish and thin crust, and there's a few locations in the city, two are downtown.
I'm happy to give other recommendations if you're looking for anything else.