Do magic schools or colleges exist?
Many major universities and larger colleges have magic programs. Like all things, there is a very steep curve from average to the topmost tiers.
If you want to get an impression of how many there would be, consider that the Awakened make up 1% of the population (Of course that seems to fluctuate as to whether it means those with potential or those actually practicing), and mundanes can also study magic theory. This roughly the same percentage of lawyers in the U.S. So a quick shorthand would be to assume that any university with a law school has a thaumaturgy school as well. Of course, there is no Fuchi University IRL. But even then most of their people didn't go to FU. Corps pay a lot of money subsidizing programs they need like thaumaturgy and Matrix programming/design.
The terminal degree for magicians is a Doctorate of Thaumaturgy (Th.D). Almost all university programs are Hermetic-centered, at least historically even with the advent of Universal Magic Theory.
The first program to grant Th.Ds was UCLA, which remains one of the top programs in the world. The other top-tier program that gets mentioned disproportionately in fiction is the program at MIT&M.
The Los Angeles metro region universities had programs which were all competitive with each other (And UCLA). However, after someone decided to sink southern California into the ocean the only two that remained were UCLA and CalTech, which is way out in Pasadena. CalTech is also a very small university now. Those two are mentioned in Corporate Enclaves, but it's not that big a deal.
GIven Seattle's importance to Shadowrun, UW and Seattle University both have important programs (Seattle's of course being much smaller than what UW can field).
Like UCLA's influence on L.A., MIT&M has driven all the Boston-area universities to open thaumaturgy programs. So you can get a degree from Harvard, Tufts, Northeastern, UMass, BC, or BU. But really you either go to MIT&M or you don't.
The University of Chicago has a strong program that survived the Bug City years.
Georgetown (in DeeCee) named their program Occult Studies. It's also a Jesuit-run university (As is Seattle U) so there is a Catholic influence there. The other DeeCee schools have their own programs, of course.
The major CAS schools are Georgia Tech and Texas A&M. I can't recall what has been mentioned, but I know it's not much, about schools in Louisiana. I would expect Tulane, Loyola (Another Jesuit university), or LSU to have pretty good programs since New Orleans is a pretty magical city.
There's a shamanic program at Lakehead University in the AMC.
Outside North America, the big programs are Charles University in Prague (Schwarzkopf, a great dragon, is one of the professors) and Jena University in the AGS.
Do regular colleges exist?
Yes.