I didn't realize I wrote so poorly...DD is in 8th grade. She has the grades and test scores to attend a very exclusive public school that specializes in Math and Science. You must be invited to attend. They have no sports at this school. OR she can attend a very good Private school that I will pay for that does have SB for 4 years.
DD wants to play SB in college. She does not need an athletic scholarship to go to college. She plays club/tournament ball now and would continue. The question is...would your kid lose to much by not playing 4 years of HS ball. Could you make up for that on your own. Would going to the math and science school pretty much end your chances of playing college ball. Should you care that your kid might not play in college. I hear it's about the education when referring to what college to choose. Would you put your kid in one HS because they average 150 pts more on the SAT? 1950 vs 2100?
I wouldn't worry much about the SAT difference. The more important thing is the quality of the teachers, not the students. It's not always easy to measure that, though. ...
As far as sports in high school, it depends on your daughter. Mine likes school ball more than travel ball. She sees TB as something she needs to do to play quickly on a very good high school team some day. But other kids don't like school ball, especially if the school team is mediocre or worse. I'd think your daughter's personality would determine much of this.