When visitors come from out of town, try the old standbys that Chicago is known for. Many will argue that one place is better than another, but I still think it's worth trying the classics.
So that means for
Pizza: Gino's East and/or Lou Malnati's (I think that these have surpassed Uno's, though Uno's was the first, its rarely recommended)
Hot Dogs. Can go just about anywhere.
Italian Beef: Al's No. 1 is good, but again there are lots of other good places.
Greektown has some relatively inexpensive, but nicer places.
Coffee: Intelligenstia
"Breaded Steak Sandwich": Ricobene's
Chinatown has lots of good, inexpensive places
Manny's for a real Deli
There are some Polish buffets on Milwaukee Ave. (though I haven't been very impressed with them)
Not a cheap outing, but hot dogs and a baseball game (I'm not getting into Sox or Cubs, you decide.)
If you travel north, Devon Ave has some nice and inexpensive Indian restaurants, and a good Israeli restaurant.