I’m a former teacher and IMO the biggest thing to look for in a school is parental involvement. It also helps if the school is hard to get in to whether it’s public or private. Schools that make you jump through a few hoops (with lotteries and other prerequisites) weed out the parents and kids that don’t care about education.

Personally, I’m a lot more concerned about the moral climate of a school than the academic climate, but the two often go hand in hand. I’m not nearly as concerned with my kids getting into elite colleges as I am with them doing well and becoming well rounded in high school.
I’ve seen too many people with elite college degrees who have done nothing with them.