H.P. Lovecraft set his books in the New England region where he lived, and modelled a fictional university on Brown University in Providence, Rhode Island, as a setting for more than one of his stories.
It is an Ivy League school on par with Harvard University and is situated on the (also fictional) Miskatonic River in the (also fictional) town of Arkham, Massachussetts. Arkham is a fictional town whose name has been reused not only in real life (Arkham Press, etc.) but also given a nod in other media (Arkham Asylum, a mental hospital in the Batman series). Arkham is located far north of Boston, Massachussetts in Essex County.
It is where Herbert West attempted to reanimate corpses in one of his most famous stories. It's also where other characters were either schooled or performed research. Despite the notorious and scary reputation of the town and its university, it is (in Lovecraft's world) a prestigious place for the upper middle class and those who wish to reach the upper middle class to send their sons - and yes, sons. In Lovecraft's time many universities were not co-ed, but were segregated by gender.
One of its most notorious features is that it contains archaeological artifacts and occult books which, in Lovecraft's world go beyond merely representing an enviable collection of historical artifacts but is also a corpus of arcane knowledge which leads more than one person down a doomed path.
The university features more prominently in the Chaosium role playing game Call of Cthulhu where player characters, also known as Investigators, can gain power and risk madness by researching Things That Should Not Be Known in the libraries and faculty shelves of this grim place.
As a fictional place, it has been featured in merchandise, made well after Mr. Lovecraft's death. It is possible to get diplomas from the "University" as well as merchandise parodying those available from real institutions: bumper stickers that parody "my child and my money go to X university" with "my sanity and my money go to Miskatonic University", and alumni T-shirts. The merchandise is not all serious, for example the joke that their sports teams are referred to as "The Fighting Cephalopods" as mentioned above.
In all honesty, as a writer Howard Philips Lovecraft was no great shakes: he himself hated "The Shadow Over Innsmouth", whose initial publication failed to sell even though the books were discounted to the bargain price of a dollar. He had a tendency to "punt" on descriptions of things, describing them generally as "something I cannot.... must not remember or describe!!!! But allow me to continue writing this even as something from some far angle of another dimension is eating me feet first as I type this..." It bridged the gap between the supernatural horror of the 1800s and prior to the modern body horror of the slasher film and zombie genres.
What he did do, however, was create a world with memorable towns and places that exist only as footnotes or pages in his work. Miskatonic University, the town of Arkham, the towns of Innsmouth and Dunwich, the book called the Necronomicon: all of which have been referenced anywhere from other authors setting their stories in his world to shout-outs in other media - even as far away as Splatterhouse, a video game from Japan.
Now if you'll excuse me, there's a strange scrabbling sound behind the wall of my dorm room....