Dusk Maiden of Amnesia
I’m not much of a horror fan, but this anime hooked me. Yuuko is an evil spirit haunting a high school, and she is a loveable ghost that has a crush on the protagonist, Teiichi. Which Yuuko is the real Yuuko? It also delves into Japanese culture with old world mysticism clashing with new world logic. All this set in the traditional Japanese high school with clubs and funny taboos and fantastical—no adults present to control the consequences—society.
I like anime that makes you think. This one does it with the ghost story. The history of Yuuko and how she came to haunt the high school is well-told. It is blended into the current plot line and her infatuation with Teiichi, and even though you know the history part-way through, the story still manages to surprise and entertain until the end. The mystery is the ghost, not necessarily her back story.
Give it a try.