In a lot of places, it's just called The School.  In some places, it's called The Magic School; in the rare lands where there are many schools of magic, it is sometimes called Calliope's School, or The Whitlock Academy.

Sometimes it is a tall tower in the middle of the city; sometimes it is an unassuming little cottage on the edge of a village.  Sometimes it's on an island in the middle of a lake.  Sometimes it's a little castle floating on a cloud.  Sometimes it totters around on enormous metal chicken legs, wobbling ominously back and forth but never falling over.  Sometimes, in places where it is unwelcome, it is a door in a back alley that isn't there the next day, or a tunnel behind a swiveling bookcase, or a hole in the ground beneath a gnarled old tree.  On the outside, it is all these places, and more, all over the world; and on the inside, it is all these places, and more, so that even if all its outsides were gathered together in one place they still wouldn't account for all the rooms and halls and nooks and crannies you could find.

Calliope's School teaches magic, naturally.  It also teaches other things.  Crafts and trades; literacy and arithmetic; history and geography.  Sex education - this last is one of several reasons it is sometimes unwelcome.  It teaches people with magic how to control it, and how to put it to good use.  It teaches people without magic many ways that they might come to have it; and whether they choose to take advantage of these teachings or not, it will teach them to recognize magic, and understand what it can and cannot do, when to be wary and when to be welcoming and when to be curious, and always to be respectful of it.  It will also teach you about magic you can't or shouldn't use - the natural sorceries of wild and domestic animals, the ancient solid curses that live in old rocks or trees, the signs and symptoms of deliriant gods.  It teaches common arts - ensorcelry of mirrors, hedge-potioneering, and the like - and arcane pursuits - conjurations, charms and hexes, old and complex witchcrafts, how to work devices of power - and even some forbidden disciplines, like pneumaturgy or aberration of the flesh.  (This is another reason it is sometimes unwelcome.)

Calliope's School is for anyone.  The young may study there, or the old; the rich, or the poor; the human, the no-longer-human, the ought-to-be-human, the never-was-human.  The cursed or even the blessed are welcome there, as are the innocent and the guilty.  (You may be ejected, or your privileges restricted, for wrongdoing on-campus, but you will almost always be given the opportunity to learn better than the worst thing you have ever done.)  You may come to Calliope's School in order to lay bare the deepest secrets of the universe - or simply to learn to darn your socks without a needle, or ask what it's like to live in the next town over.  You may even spend the night in the School intending to learn nothing at all, if all you want is a hot meal and a warm bed, though if you spend more than one night you might end up learning useful or interesting things whether you like it or not.

Calliope's School, like its reigning headmistress, is a little over three hundred years old.  It has been growing bigger all that time.  Not everyone thinks that this is a good thing; but there are many, many stories, more every day, about it changing lives for the better.