In my new setting (the Border Realms), there will be three different large schools/libraries spread across the continent: Ziris in the west, Endrion in the east and Nova Draodheas near the center of the map. But I'm having problems making the three schools distinct. I have a bit of an idea of how a fictional school is supposed to be, so I'm struggling with breaking out of the mold. Here's what I'm working with so far, any new ideas would be greatly appreciated:

Ziris is in the capital of the Zir nation. Since Zir is mostly a nation of Dragonborn, the school is a bit exclusive, and its library is pretty focused on draconic lore.

Endrion is a school of pretty much everything, although mostly magic. Its library is famed across the entire continent of Luinaren, but it's also very controlled by the local magic guild.

Nova Draodheas is the new kid on the block. It was founded after the Tiamat crisis (Tyranny of Dragons) by the archmage Malvedar (who later became a lich, not all that important) and intended as a sort of middle-ground. It's magic focused, and has one of the largest libraries on the continent, although said library pales in comparison to Endrion. It's also less political than the other two. It's headmaster Malvedar (they just refuse to die, for reasons stated above) obviously keeps an eye on the happenings of the realm, but it's not affiliated with any nation or magic guild.

Start with what the culture of the areas is like. If the Dragonborn of Ziris are exclusive and focus on Draconic lore, then maybe include descriptions of oppulence as the Dragonborn emulate the hoards of true dragons. Do the students come from nobility? In that case, martial prowess might be important to them as they try to prove themselves. Swordplay might be taught, alongside a cirriculum with a preponderence of evocation spells. If so, perhaps the heritage of the Dragonborn is a factor in which classes they are assigned.

Is Endrion ruled by the Mage guild directly? If not, there may be an air of discontent centred on the students who were admitted by and/or inspite of the guild. Perhaps there are some guards in the library, whether humanoid or some golem, or even elementals.

Nova Draodheas is led by a lich? Is this common knowledge? If so expect some do gooders dropping by. Is necromancy taught? Are they being courted by nations and guilds?

In general, perhaps include a specialty for each school,  an area they are lacking in, maybe even trawl around for a special spell, taught in each school, homebrew or just reskin a spell to look or act different (a fireball shped like a dragon's head, or a cause fear that is actually a conjuration spell summoning some energy from the Shadowfell). Is there a specific quality looked for in new students, in true Hogwarts style? Are the schools and students competitive, in school or between the schools, and if so, are contests held? Are there famous students/staff that the schools admire.

This sounds very cool, and I hope this helps.

Maybe the different schools have different attitude toward magic. Maybe one school practice an almost religious rigor to the study of magic, their students cloistered away as is part of a monetary, studying in solemnity. Meanwhile in one of the other schools, magic is just another tool to be honed, practiced, and innovated upon for whatever end can be dreamed up. Maybe the third school doesn't only teach magic, but magic is just one of their varied curriculum, also including the other arts and sciences and maybe even other adventuring skills. 

Try to think what the "mission" of each individual school would be. Mission as in mission statement, not like any secret agenda or anything.