I see two Dennis' Place listed in the phone book.
DENNIS PLACE FOR GAMES
6701 N CLARK ST, CHICAGO, IL 60626
(773) 743-5207
DENNIS PLACE FOR GAMES
955 W BELMONT AVE, CHICAGO, IL 60657
(773) 528-8616
Fun Zone on Western ave. was one of my hangouts as a teen (22 years ago and still in business!).
FUN ZONE
3641 N WESTERN AVE, CHICAGO, IL 60618
(773) 528-3032
There is Dave and Busters on Clark
DAVE & BUSTERS INC
1024 N CLARK ST, CHICAGO, IL 60610
(312) 943-5151
The GameWorks in Shaumburg is accessible by public transportation.
Most malls around here will have a small arcade.
Union Station has a small (6 to 8 games) arcade next to the Grand Hall.