I've lived in Chicago all my life. This crooked city and county sucks. The best public lands imo are the ones south of I-80. I'm not a fan of the ones near the city and surrounding suburbs. If you go public, be prepared to put in some work. There is a 25 yard archery range/shop in Oak Park and a really good one out west near aurora, at a park district. I don't do deer shotgun, since I like the longer bow seasons.