You’ll get there through the main story
If you’ve read any other Hogwarts Legacy guides, it’s no surprise that many aspects of the game (mechanical and lore-wise) are locked behind main story quests. Whenever you have one available, it’s smart to do them, so you can open up more ways to play, and more places to explore. That includes the hospital wing, which opens as a result of a mid-game quest.
The hospital wing is unlocked through the The Caretaker’s Lunar Lament main quest
Following the story mission “Percival Rackham’s Trial,” you’ll be able to take on “The Caretaker’s Lunar Lament,” which is marked as a main quest (with a yellow icon). This is the questline that teaches you how to open all of those pesky locks you’ve seen throughout the game, and the tutorial lock is the doorway that actually leads to the hospital wing.
You’ll be using the Disillusionment (cloaking) spell to go up a few levels (remember to use the basic cast against the wall to distract NPCs, or talent into the stealth three for an easier time with this): ending up in the hospital wing. After you arrive, several key characters from the campaign will be talking among themselves. Cast Revelio when you’re in the room (note the chests to grab): your character will whisper it and it won’t alert anyone.
Following that, you’ll be able to find it in the same location!