Meanwhile in the book, the index tells of a Research Desk (Experimental), which is written about in the beginning of the book in Magister Rowan's clear, bold blackletter calligraphy, with cramped margin notes and page references added by Magister Aspen. Apparently it might be able to summon fragments of notes from other destroyed towers using Lightning magic, but Mg. Rowan's prototype was destroyed by, ironically, a literal lightning strike from the sky, and they didn't have the materials to rebuild it before the fog came; therefore the best Mg. Aspen can say about its verifiable functionality is that bits of paper did appear out of thin air and Mg. Rowan did seem really excited about them. It's best placed in a room with a lot of bookshelves (page reference for how to use Nature and Air magic to process wood into blank books, plus a little Dark to get the leather for the covers from an animal carcass; Mg. Aspen assumes whoever inherits their wand can figure out making shelves out of wood on their own).
There's also a Gruel Pot, useful for making simple stews, and a Dragon Wok, for more complex cuisine; Mg. Aspen advises constructing a room to hold both even before you have the materials for the Dragon Wok, and adding this nifty wall-mounted spice rack that not only helps you keep your ingredients organized but also has a bit of Air magic worked in that actively helps you pick up the right containers from across the room smoothly while cooking, and ambiently enhances the magic of the cooking pots.
Here's a page on how to make magic beds, and what kind of decor gives them ambient enhancement; the key is apparently rugs, and proper lighting, none of those dim flickering smokeless torches (page 98) like the ones in the underground chambers.
The elemental focuses for Apprenticing in secondary elements each need their own room, ideally with bookshelves and element-specific decor, but Mg. Aspen doesn't actually know the full procedure for building them all and several of the components they do know about are going to be hard to reach from this hilltop. Which leads into...
Alchemical Beasts! Indispensable for automatic processing of raw materials into other stuff. The easiest one to make is a Midden Jelly, which separates out and preserves all the most useful bits of a small animal carcass. More advanced ones for making things like cloth or glass or iron require multi-student rituals which Mg. Aspen has never personally seen, though they've dutifully preserved and organized Mg. Rowan's notes on the subject. Oh, and you can also use them to process, um, you know, certain things, into fertilizer. Here's a page reference to a section on installing plumbing. You can use Water magic to get running water, and Fire to add heated water for baths and so on.
Speaking of rituals, any good magical academy needs an Auditorium with a proper ritual circle for Graduations! There's an entire section detailing how to construct the ritual circle and all the proper decor to ambiently support it, cross-referenced back and forth with the page describing the ritual itself. Mg. Aspen notes that many other academic rituals are possible but this one is the only one you really need.
Medical Beds! You should have an Infirmary, in case of attacks by gribbly creatures from out of the fog (has only happened a couple of times, but they were very memorable) or whatever is happening in the Underschool (Mg. Aspen says that Mg. Rowan's notes were planning for taking a force of a few mages down there to investigate, as soon as they could summon that many students, which they never managed). Here's how to make a Medical Bed and the Incense Burners that serve as supportive decor, and notes on a few Medical-Bed-based healing rituals which, Mg. Aspen's margin notes cannot stress this enough, should be carried out by a Magister. You can cheat on some things but you cannot cheat on the level of channeling control that goes into your healing ritual.