I know it's a chain, but I'll throw Fleming's in there as well. They have a great happy hour every day- including the weekends from 5-7pm, where their listed cocktails are all $6. Their burger which comes with bacon and cheese is delicious and for $6, quite a bargain.
Hi, I recalled this article from Chicago Ragazine. Found it pretty interesting, I read it a few times:
These are pretty close options for you
500 N. Clark St.
David Burke’s Primehouse
616 N. Rush St
District Bar <Very quick walk>
170 W. Ontario St
The Capital Grille
633 N. St. Clair Street
500 North Clark St., Chicago, IL 60610
5340 N River Rd, Rosemont, IL 60018