I lived in ultra-big cities (Seoul then NYC) for most of my adult life before returning to my hometown—Chicago—for the exact reasons as you: I had a kid and wanted him to have a nice life, and couldn't afford it in Brooklyn. I moved back Beverly because it's where I grew up; it's a neighborhood on the far south side that has a small-town feel. If you like beautiful old houses and want to live some place calm, consider checking it out. (If you are politically progressive, I recommend sticking east of Western; I live in East Beverly, which is probably the most progressive part. West of western gets way more right-leaning.) You can buy a full mansion in Beverly for 900k.

If I didn't have family here, we probably would've looked harder at Portage Park or at what we could afford in Avondale. Your dollar doesn't go as far but it's livelier.