Then I would nominate Hawthorne's "Feathertop"—for reading in the schools, and perhaps "Young Goodman Brown."
I think his "Rappaccini's Daughter" is an excellent story, as is "The Birthmark," but whether they are fantasy or science fiction may be up for debate. So-called scientists drive the stories, but they really appear to be more like magicians, so they could be either, really.
"The Lost Room," by Fitz-James O-Brien, and any one of a great number of stories by Algernon Blackwood.
I'd add Hawthorne's "The Artist of the Beautiful." And I'd at least consider Blackwood's "The Willows".
Some required reading I hated, like
A Separate Peace; some I really enjoyed, like
Of Mice and Men. Some of those Hawthorne stories were required reading; “The Tell-Tale Heart” was required, too. So, I have nothing against required reading, as it becomes a shared experience and if the teacher is good, one that requires discussion of why one person likes it and another doesn’t, and why the teacher would assign it in the first place.
Stories I'd have a class read (if anyone was daft enough to let me teach):
"The Homecoming" and/or “The Foghorn” by Ray Bradbury (the latter for its mood; the former because I think it could be tagged as a precursor to everything from "The Goonies" to "Stranger Things.” I recall reading “The Veldt” for class in grade school, so Bradbury isn’t a far reach.)
“The Happy Autumn Fields” by Elizabeth Bowen (beautiful prose in service to a mood piece based on reaction to the then current WWII)
“Ghost Summer” by Tananarive Due (for high school, probably; an example of how to take a serious subject and present it entertainingly and even with humor)
“Linneus Forgets” by Fred Chappel (for high school; a masterclass in merging the historical with fantasy)
Not sure what, but probably something from Sussanah Clarke, Theodora Goss, Angella Slatter and/or Kelly Barnhill, all of whom work around the fairy tale as examples of how fairy tale and folklore inform fiction. Maybe for high school juniors or seniors something from Angela Carter for similar reasons. Or possibly Patricia McKillop’s “The Lady of the Skulls.”
I suspect, if I think awhile, I’ll come up with some others.