Unless the area is fenced in and locked all public schools are fair game. A few rules I follow when hunting schools:
1. Take a plastic bag with you and carry out all trash you find. Most of the time there will be trash cans around somewhere.
2. Never detect when kids are present unless they have a responsible adult present with them.
3. Never detect during school hours and try to wait at least one hour after school. Most teachers are there until at least an hour after and some of them get nervous when they see you messing around.
4. Always recover your holes to the best of your ability.
5. If you find anything questionable, needles, bullets etc out local prinipals want us to call and let them know. The school is installing cameras and such to monitor after hours activities and some locations are cracking down on criminal activity. This is of course up to you but I try to honor the request made by the principals.
6. Try and stay away from the actual buildings when it starts getting dark. Had a police officer check me out once because it was almost dark and I was detecting pretty close to the buliding and he said I looked "suspicious" A six foot one inch guy swinging a detector with a light on his head looks suspicous for what other activity other than metal detecting
Enjoy your hunts you will find a lot of interesting items. One last piece of advice, dig every signal. You NEVER know what you may find.