Here is a sampling of my favorites:
"The Horror at Chilton Castle" by Joseph Payne Brennan--This story is an interesting variation on the strange tale of the hidden room at Glamis Castle, seat of the Lords of Strathmore. Supposedly when the earl's heir comes of age, he is taken to the hidden room by his father and the castle's factor and sees something so horrifying that his hair turns white, or he never laughs again, or he goes mad (a little hard on the succession). The fifteenth earl, great-grandfather of Queen Elizabeth II, reputedly stated: "If you could only guess the nature of the secret, you would go down on your knees and thank God it was not yours."
Substitute the fictional Chilton Castle for Glamis Castle, and be prepared for a shocking explanation of the secret room.
"Heartburn" by Hortense Calisher--It's generally a bad idea to mix horror with humor or irony, but this story manages the mixture rather nicely. A psychiatrist at an exclusive boys' school sets out to discover the reason for a sharp decline in morale, which seems to affect all of the students. His curiosity results in a severe case of heartburn.
"Nursery Tea" by Mary Danby--An old nanny is invited to tea by her ex-charges, who are not as fond of her as their parents seemed to believe.
"If Thy Right Hand Offend Thee..." by A. E. Ellis--Another tale of a boys' school, this time in the manner of M. R. James. During a séance, a student lapses into a trance, and a grim visitant begins to haunt the school. What can it possibly want from Mr. Matthews, the biology master? Why is it so interested in cutting instruments?
"The Spider" by Hanns Heinz Ewers--Three suicides by hanging on successive Fridays leads a curious medical student to rent the hotel room in which the deaths occurred. Not a good story for arachnophobes.