I'm trying to remember the author and/or title of a sf short story featuring a mile high skyscraper that was an economic failure, so only the lower floors were in use - until the protagonists find aliens using the upper floors. I remember it from the 70's or very early 1980's, but I suspect it was written in the 1950's.
Several months late, but is it The Far King by Richard Wilson?
It is a very odd sci fi story featuring aliens living almost normal human lives in the upper floors of an abandoned skyscraper complex. I believe the complex was called something like the "Mile High Tower" or something similar. One of the aliens was known as "the Black Magician," the two protagonists were former high-school sweethearts and lovers, but the female became obsessed with human-looking prince from a planet literally called "Far Land." The prince, however, was homosexual, with his lover named "Neel" or something close, and gave the woman a vial of his sperm so she could sire his child. As humans and Farlanders weren't actually compatible, the sperm was really human sperm donated by the male protagonist when he was low on money at a local human sperm bank.
As I said, it was a weird story, but it fit the details you provided. The time period is correct, and it was published in several short story anthologies edited by Isaac Asimov. I have it in his Comets and Computers, but it's also in Asimov's Science Fiction Magazine, March 1978.
I could be way off on this bizarre - and not, in my opinion, very good - sci fi story, but the reference to a mile high skyscraper makes me think this is it. The full text doesn't seem to be available online, and I've never heard of Richard Wilson ever doing anything else. I suspect this was one of a very few sales for him in that period, and he's kept it under copyright because he's not making money from writing any other way.