As a native Chicagoan, I agree with many of the above posts:
Lou Mitchell has the best omelets in town. Make sure you try the homemade orange marmalade.
Berghoff is excellent.
Greek town has many good places including Greek Islands & Rodity’s.
Italian beef is the best at Al’s on Taylor (open late) or Mr. Beef on Orleans (lunch only.)
Excellent steak at Gene & Georgietti if your expense report can handle it.
Kaufman is a good Jewish deli but being in Skokie makes it a real schlep. Try Askenaz on Cedar just off of State Street.
For a sweet treat, try the smores at Mr. Kite at 1153 N. State around the corner from Askenaz.
My favorite lunch is at Manny’s. Everyone raves about the corned beef which is very good. But I prefer the roast beef. It is the only place I know where you can get a carved roast beef sandwich.
Hope it helps.