It really depends though. As a parent raising kids in the city myself, my wife and I made the conscious decision to settle in the city and raise our family here.
We based this on:
0) We just really like the city and want to raise our kids in the city.
1) In Chicago, where we live, CPS students outperform the state overall. Source:
https://www.wbez.org/shows/wbez-news/perception-vs-reality-c...
2) Breaking down a school's performance at the demographic level can often change the equation. The elementary school my son will attend actually scores higher for students above the poverty line than the one I attended out in the suburbs.
3) My wife is a STEM professor and has seen lots of students who attended the region's top-tier public schools (9/10 or 10/10 on greatschools, etc) that were woefully unprepared for college, despite otherwise decent ACT scores.
4) The suburbs are facing their own austerity crisis: postwar subsidized infrastructure gravy train is long over, so property taxes are rising. Their housing stock doesn't align well with the smaller and most cost-conscious millennial family. So a big worry for us was, do we want to buy into a "good school" suburb only to have our kid's school budget slashed to control costs? This is already happening to one Chicago suburb famous for its great schools (Hinsdale, IL)
5) School performance is, at best, a trailing indicator. Say you've got 2 kids under the age of 4. Is it worth buying a home somewhere because of a high school they won't be attending for 10+ years? It makes sense if you're talking about a radical difference in school performance, but marginal advantages seem prone to change.
I don't claim that this is the best course of action. For all we know, the city schools could just as easily go sideways due to budgeting issues, or maybe suburban schools are the first to break free from the trend of "teaching to the test" and our kids are left behind. But right now, it just feels like once you have a safe learning environment and some basic academic standards, most of the outcome is in the hands of the parents and students. High-performing schools don't produce great students so much as they attract the people who foster that attitude.