I see you are on Western Ave. right by Crabby Kim's. I grew up there and still have friends there with cars. Maybe you know Jay with the yellow American Graffitti Ford. Cool car you have there.
The local ones are unfortunately not in the city, but they are in the surrounding burbs. Here are a few that I can confirm are going on. I have a list of more but I have never been to them so I cannot say if they are good or not.
Monday- Westchester at 31st and Wolf Rd.
Wednesday- Downtown Elmhurst
Friday- Windy City Rods at 6143 W. Howard in Niles. McDonalds in Rosemont at River Rd. and Higgins under the Rosemont water tower.
Saturday- Downtown Mt. Prospect on Northwest Hwy. (good show) Bouna Beef on Arlington Hights Rd. in think Elk Grove Village but it may be Itasca