Well, NYC would exist in the Harry Potter universe, though, just like Australia and Germany would... they're just not mentioned, because the story's set in England.
I don't "do" fanfic, but I'd have thought an alternate universe would be more like, Harry Potter set in NYC in the year 2378... or a story about Hermione ending up in Middle-Earth... or a version of Harry Potter in which Snape managed to bring Lily back from the dead, or Neville was the Chosen One, or some other plot change that altered the premise of the universe and/or the way events transpired. That last kind answers questions like "What if only women could do magic?" or "What if Ron became a Death Eater?"... it's more than just making up events that are consistent with the canon, like describing one of Harry and Ginny's "dates" in sixth year.
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