Which city has the better public school system and quality of life: NY or Chicago?

I go to graduate school in the bay area. Once I finish, I want to settle in a big and very diverse city outside of California with my child. San Francisco is way overpriced for a city that is earthquake prone, dirty and full of homeless ppl sleeping and shitting everywhere. I grew up in Chicago and I think it's perfect for me. I also like NY b/c there's so much to see and do.