I figure the basics would be:
Teaching of paramagical skills. (So this is where you get training in Arcana, Concentration, Spellcraft, or what have you, based on the exact edition.) Higher-"level" classes would teach more esoteric skills, such as Knowledge (the planes). Night classes might be offered to experts, bards, and what not. Some of these classes might not be taught by casters, but by experts. This seems to be the area you're focusing on. "Care and feeding of level-draining plants" might be a 4th-year course.
Looking at this page is handy:
http://www.d20srd.org/srd/skills/knowledge.htm
Here's what it says about Knowledge (arcana): ancient mysteries, magic traditions, arcane symbols, cryptic phrases, constructs, dragons, magical beasts. Each of those could be a course.
Teaching of languages. A caster might find Draconic and Elven to be useful languages. Dwarven, probably not so much.
Teaching of spells. First you have to teach Read Magic, and then cantrips, and then so on. (Details depend on edition, of course.) Higher-"level" classes might feature different schools of magic, or different traditions. What is the typical level of a graduating mage? IMO, it should be 1st-level. However, there might be "graduate school" for higher-level academic wizards. (A typical adventuring wizard might have a Bachelor's in Arcane Arts.) Also, some schools of magic or applications might be banned. (Banning the summoning of imps or the animation of the dead come to mind.)
Teaching of rituals. (This may be separate from spells, depending on edition. In a 4e world, the different categories of rituals might have their own classes, eg Creation Rituals 101.)
Teaching of tactics. Some academies might not teach these, or be restricted in what topics they can teach.
Teaching of ethics. (Might be considered "unnecessary" or "impractical" in, say, Thay, or by the drow.)
Teaching of magic item use. Teaching of magic item creation. (In a 3e-world, Scribe Scroll might be taught as a 2nd-year course.)
In a 4e world, teaching of implement types.
Are these schools inclusive? Do sorcerers and wizards go to the same school? Bards? Assassins? Do elves have their own schools? Do you accept foreigners (eg if you're almost at war with a neighboring orc tribe, do you accept their scholarship student)? Are there lots of little specialized schools, or just one big one per major city?