If you're concerned with youths being a problem, why not "magic college"? That way it gets you away from the idea that the people here are primarily under-age and also gets you away from the idea that only young folks get trained here. A magical "college" could train the young, the old and everyone in-between, further, the party could then become a mix of students and non-students alike. Graduates, drop-outs and people who never attended, all being pulled in to the adventure for Strange Reasons! If you'd like the party to be non-students but have a good reason to be at the school, they could be "summer intern" types, coming back to train one-on-one with a specific teacher in exchange for them providing free labor to the school (like receptionists, RA's and other kids on college campuses).
Personally I'd say the "boarding school" concept would be beneficial to keeping the campaign restricted to the college grounds.
If you're going for an "everyone has gone missing and the party has free reign of the campus" I'd definitely contrive some kind of magical ward that locks them in once they arrive. All the better if they only go there because Jimmy was all "Hey man lets check out my old stomping grounds, I bet there's some sweet magic stuff and we can score some hot magic college babes!" only to arrive to find the place desolate, deserted and with scattered signs of a struggle. (which makes the whole thing rather dark ya know?) Of course, new blood arriving triggers the "silent alarm" which locks them all on the campus, and of course, awakens whatever decimated the school population. Depending on how recently this occurred you could have all sorts of fun additions, unchecked experiments gone wild, magical looters (who may or may not have a way out, but certainly don't want to get caught!), rogue magical sentinels and of course the BBEG.
IMO: you've got two solid options here:
A: the "college" vibe. It's a functioning college and your party members are college students, why they weren't affected by the "Event" is an important question on the adventure. (On this line, there should be a couple other people unaffected, just to help cast suspicion about).
B: the "scooby doo" vibe. Your party are not current members of the college, but when they pay it a visit, they get ensnared in the aftermath of the "Event".
I think, most importantly, will not actually be the campaign itself, but the layout of the school. Magic "schools" have an abundance of traps, locks, hidden doors, secret rooms, moving hallways and shifting floorplans. You're basically running a maze that to some degree, moves and changes. Simple clues could be misplaced across the entire structure because the Mr Mustard did it with the Candlestick in the Ballroom...but the Ballroom sometimes enjoys the sunset and moves from the north east corner of the building to the south west and the Candlestick really dislikes the south west.
