Screenshot from Little Witch Academia, by Studio Trigger
Any supernatural academy worth its salt is expansive enough to be a community in itself. Dorms for living space, an expansive courtyard connecting the many buildings, a humongous library full of lore from all over the world... all that's needed left are some dungeon-like environs!
The Obstacle Course: If the adventuring occupation is a common vocation in your campaign setting, it's probable that there's enough demand for it by mages wishing to pursue the arts of spelunking and tomb-raiding. Classes for amateur adventurers need a lot of space to test the abilities of fledgling apprentices, and a series of underground interconnected chambers is perfect for this!
The adventurer's classroom would be accessed in a dark and relatively isolated part of school, guarded by a set of iron bars, below a massive trapdoor sliding open to reveal stone steps leading into the earth, or accessed via teleportation to a mysterious location. The teacher sets the students in groups of 3 to 6 (the average adventuring party size) to work together through the series of rooms. They will be graded based upon the amount of treasure they obtain; how many traps, puzzles, and monsters they successfully bypass by stealth or by force; and how many team members make it through to the end.
The teacher hands out circular armlets for students to wear. This allows him to easily scry upon them, so that he may accurately judge their progress as they make their way through the dungeon.
The Forbidden Library: It's a well-known fact that power corrupts, how certain knowledge can be corrosive to the mind and soul of those unprepared for it. Even on a more practical level, certain spells such as fireball are capable of great destruction, and students lacking the ethical mindset or experience may be denied the opportunity to learn such arts until they're deemed ready for it.
Thus the need for a forbidden library. In here are tomes of the dark and macabre: here you might find Aris Blackheart's Guide to the Lower Planes, A Treatise on Eugenics & Bloodline Sorcery, or the Song Spells of the Derro Sages. There are no windows in this cordoned-off space, and the light spells are few and far between leaving the majority of the halls shrouded in darkness.
The Forbidden Library's caretaker might be a mischievous spirit known as Parva Darkwater. The library's forbidden nature only encourages curious students to sneak their way in, and he has lots of fun using illusions and misdirection to scare them and thus preserving the library's frightening reputation. Or it might be a wizened crone who bears a striking resemblance to an infamous necromancer; when questioned on this mentions that she does not want to see others go down the same path she did, consumed by the follies of lust for power at the expense of restraint and insight.
The Ruins: It is a rule in fantasy worlds that the marvels of the ancients never truly end. The animating magics of a long-dead empire of mages beneath the sands might still churn on: summoned familiars dart between decaying towers home to the skeletons of their masters. War-golems patrol the empty streets, on the lookout for threats which might never come. A group of enterprising folk who manage to clear out these old structures of danger will gain an invaluable asset.
In this scenario, the magician's school is built upon the bones of the old and dead, a core of the old-world protected by a shell wrought by century's worth of expansions. With the treasures and lore of the first ones the mages were able to turn this building into a center of arcane learning without peer. But the truth is that the school's founders were only able to claim a portion of the ruins, the majority still remain sealed behind powerful wards. The school regularly sends out exploration teams into the catacombs below with limited success. There is precious little to be found in the already-explored reaches, and many folk are unwilling to breach the wards in case they're containing something dangerous. In the shadows of the ruins and sometimes the school above, people spot oddities. A slithering shadow, a quick rustle of air from an unknown source, the dripping of water in a dry room. Just what did the buildings' original inhabitants have in mind when they built the old structure, and what did they seal away before their demise?