From the entrance, the first room to the left has a Novice Faculty terminal and an Advanced-locked door. Open that door then access Principal Tanner's Terminal. You can use this terminal to open the next door. Don't forget to loot the Library Key from Principal Tanner's desk.
There's an Overdue Book inside a stall in the female restroom across the principal's office, a chem station in the class room to the east. The second level classroom on the eastern side also has an Overdue Book on a desk, and you can get the Principal's Office Key from the lunchbox beside the student terminal. This key is worthless if you already unlocked Principal Tanner's desk and storage.
In the cafeteria, there's a door leading to the basement beside the milk bottle machine to the north. There's a lone supermutant hound inside and several meat bags that may contain random loot.
Make your way to the second level head south. The first classroom to the right has another overdue book. The green double-door to the north can be accessed using the Library Key. There are some scattered mines and trap in the room as well as a book return terminal which sadly, doesn't contain anything worth spending the tokens on.
The small room to the NW has a red steamer trunk, armor workbench, several overdue books on the table, and an issue of the Unstoppables. The locked room beside that can also be opened with the library key. The only thing notable inside is the holotape Property of R. Burton. Once done, you can now leave this location.