For deep dish pizza in Rosemont, there's both Giordano's (at River & Higgins, right in the heart of Rosemont) and Gino's (not even a mile east of Giordano's, in an office park accessible from Higgins, west of Cumberland). Both are very good, not great, in my opinion.
For excellent hot dogs, there's Gene & Jude's (steamed) at 2724 N. River Road (south of Rosemont, but not very far) and Paradise Pup (charred) at 1724 S. River Road (north of Rosemont, and again not very far). As you probably know from this board, the Pup has awesome burgers and the best chicken teriyaki sandwich I have had.
For beef, there are (in my opinion) only 2 good beef places near Rosemont: 1) Johnny's (the best beef around) in Arlington Heights, just off 90W on Arlington Heights Road, and Bob-O's (excellent beef) on Irving Park just east of Cumberland. There's always Al's on Higgins just west of Cumberland, but the beef's not very good at all and it's only about 5 minutes away from Bob'O's.
Hope this helps,
Brad