One interesting story could be about an exchange student from Hogwarts going to Beauxbatons. The cultural differences between the two schools create a lot of humorous and challenging situations for the main character. For example, the different teaching styles and social norms at Beauxbatons make the Hogwarts student stand out and have to adapt in unique ways.
Wattpad also has some interesting 'Harry Potter Other Schools Fanfiction'. Some of the stories on Wattpad are unique and written by emerging writers. However, you might need to do a bit more sifting through the content as it has a wide variety of works, not all of which are strictly 'Harry Potter' related.
One plot idea could be a student exchange program between Hogwarts and another magic school, like Beauxbatons. The students face cultural clashes and new magical teachings. For example, a Hogwarts student might struggle with the more refined and elegant magic style of Beauxbatons.
One popular one might be the ones that focus on the Durmstrang Institute. They often explore the darker side of magic that Durmstrang is rumored to teach. For example, a fanfiction could be about a Durmstrang student who has to deal with the stigma of his school's reputation while also trying to prove himself in a more positive light.
One interesting fanfiction could be about an exchange program between Hogwarts and Beauxbatons. In it, students from both schools learn about each other's cultures and magic in unexpected ways. For example, a Hogwarts student might struggle with the more refined and formal magic taught at Beauxbatons, while a Beauxbatons student could find the chaos of Hogwarts a bit overwhelming at first.
One reason could be to escape the constant danger at Hogwarts. Maybe in the fanfiction, Voldemort has found a way to infiltrate the school more easily, and the Order of the Phoenix decides it's safer for Harry to be elsewhere. Another reason might be a falling - out with certain teachers or students. For example, if there are false accusations against him and he doesn't feel supported, he could choose to transfer.
Fanfictions often create scenarios where Harry Potter or his friends visit other magic schools. For instance, Harry might be invited to give a talk at Ilvermorny about his experiences with Voldemort. This would show how his story and the reputation of Hogwarts are perceived in other magical educational institutions.
One great fanfic idea could be Harry Potter attending Beauxbatons. Imagine Harry in the elegant French school environment, learning different magic styles. He might struggle with the more refined and artistic approach to magic there compared to Hogwarts. For example, their flying lessons could involve more graceful and acrobatic broom maneuvers.
One reason could be to escape danger. Maybe Hogwarts is facing a new and extremely powerful dark threat that even Dumbledore can't fully protect the students from. Another reason might be for a unique educational opportunity. There could be a school in another part of the wizarding world that offers a specialized curriculum in, say, ancient magic or magical creature training that Harry is interested in. Also, it could be due to a conflict with certain students or teachers at Hogwarts. If there are people constantly causing trouble for Harry, he might consider changing schools to have a more peaceful learning environment.
One reason could be that he wants to escape the constant danger at Hogwarts. Maybe he feels that Voldemort's influence is too strong there and he needs a fresh start. Another possibility is that he has a falling - out with some of the teachers or students, and he decides that a new school environment would be better for him.