People mention “the american wizarding school” re: Harry Potter but assuming there’s a generally constant ratio of muggles to wizards throughout the world America would need at least five schools equipped to service the same number of students as Hogwarts in order to accommodate the whole population
Plus, there’s the geographic concerns. The entire UK is about the size of Kansas. It wouldn’t be practical to have five Hogwarts-sized schools for the entire United States, each one serving an average of ten states. It would make more sense to have a lot of smaller schools peppered across the country.
There might be a few magic schoolhouses in the larger metropolitan areas, I’d guess the small towns far away from the city, the ones with a muggle population of maybe 8000 people and a wizard population of a few dozen maximum would have a town witch or wizard who would act as an after-school tutor for the handful of magical kids. I can only imagine that they would claim they were taking lessons for the clarinet or some other made-up instrument, and then a few of them would remain in their hometown to become the new tutor when the old one died.
I also imagine there’d be a fair sight more magic homeschooling here. As an immigrant nation built on the genocide and forced assimilation of Native Americans and the enslavement of Black Americans, there would be a lot of witches and wizards trying to keep their heritage alive. There would be elements of Santeria and Voodoo and other Native and West African magic, plus any non-Anglo-Saxon Old World magic that immigrants and their descendants would be trying to maintain in an increasingly homogenizing American culture.
Anyhow, this post sort of got away from me, but my point is that the Salem Institute would logically have to be only one of dozens if not hundreds of magic schools in the United States