Wizard City was a world designed with more than just storyline in mind, that's pretty clear. It was also made with lore. Maybe not as interesting as KT or DS or CL, but lore nonetheless. So here are the hostile zones in WC:
Now these correlate with , , , , again, & . Now since we only have schools for those 6, it makes sense for it to stop there. But that's just hostile areas. These are the other areas:
The Commons. Ravenwood. Pet Pavilion. Shopping District. Olde Town. Golem Court. Nightside.
Well the Commons don't exactly need a specific magic, so we can call the Commons . But I'd call Ravenwood as it's home to every magic that makes up . The Pet Pavilion encompasses pets of all schools (Except Astrals & Shadow hint hint), so it can't exactly be specific. Nightside is a place of & , Shopping District & Olde Town don't really have magic about them either; but what about Golem Court? A tower, could have been the tower for a school. Dragon Mouth Cave, perhaps the old teacher took pity on the dragon and offered them refuge there. Lots of space, there could've been a school. The Registrar & Gardening Instructor work there, most likely recent positions for them.
So what teacher takes pity on/likes Fire creatures, no longer teaches and could be associated with Golems? Gretta Darkkettle; Ravenwood's retired Alchemy teacher.
I might add more to what I think Alchemy should do, or maybe even detail a quest line to lead us there, but let me know you guys' thoughts on this in replies. Let your imagination go wild.