I'd recommend asking the schools for their average ACT/SAT scores, because those tests are standardized across the U.S. Whatever you do, don't assume that a school rated as a "10" in one state by Greatschools is the same caliber as a "10" in another state: community.greatschools.net/advice/184/Helpful-websites-when-seeking-info-about-HOW-SCHOOLS-COMPARE-STATE-TO-STATE-

Thanks so much. Great answer and I'll ask those questions.

Thanks...I was wondering about those scores and how it was all done.

You really can't. It would make our lives easier if we could but there's only one statistic that correlates with the quality of schools in these times and that's the socioeconomic status of the families that send their children to them. Public schools in affluent areas will Always have higher test scores on any test than those of public schools in less affluent areas. For all our talk, bluster and billions of dollars spent, there's sadly no comparison between schools in better areas and schools in less than better areas.
If you really want to compare schools, you've got to go to the new school and spend a day there. If you have choices, go to the several schools from which you can choose and spend time in each one. You can look at their SAT or ACt scores and try to compare them but their scores will reflect the families' incomes. You can look at where the kids are being admitted to college but most colleges try to accept a student from almost every decent school.
You could ask about teachers' strikes but no one will like the question much. When was their last teachers' strike? Some states have more than others and some districts are more militant than others. Personally, I don't like the turmoil that's created in schools by strong teachers' unions but that's me.
I do like small class sizes but those statistics are easily fudged. All school figure in their janitors - believe it or not - when they came their 'teacher/student ratio'. To know what their real class size is, you have to go see for yourself.
Good luck.

Thanks so much for this very in depth answer. It is most helpful for a very concerned grandparent.
Polly