Well, she might face new challenges. In a different school, the curriculum could be completely different. Maybe she'll have to learn new spells or magical theories that are unique to that institution. She could also meet new friends or rivals. There might be a different social hierarchy compared to Hogwarts, and she'll have to find her place in it.
Perhaps she'll meet older, more experienced students who can act as mentors. These students could introduce her to secrets of the new school that are not easily accessible to newcomers. They might also help her with any homesickness she has for Hogwarts.
In this fanfiction, Hermione could be on a mission to retrieve a valuable item from Gringotts. It might be an heirloom of her family that was wrongfully taken and stored there. Along the way, she has to face many challenges like dealing with the goblins' tricky rules and overcoming some magical traps. She may also meet some unexpected allies or enemies within the vaults of Gringotts.
Maybe he would use his detective skills to solve school mysteries, like finding out who stole the cafeteria's best cookies.
In an 'Ash goes to school fanfiction', Ash might make new friends at school. He could encounter different Pokémon - related challenges in a school setting, like having Pokémon battles as part of a school competition.
In this fanfiction, Harry might encounter new magical creatures unique to that country. He could learn different kinds of magic that are practiced there. For example, if he goes to a country in Asia in the wizarding world, he may discover spells related to nature spirits which are not common in his homeland.
Well, in the new timeline, Harry could find that Voldemort has already won. This would mean he has to figure out a way to either change the past to prevent this future or find a way to defeat Voldemort in this new, much more difficult situation. It would be a huge challenge for him.
In this fanfiction, Percy might encounter different versions of his friends. For example, Annabeth could be a powerful sorceress instead of a strategist. He could also face new and strange monsters that are unique to that universe.
Well, he might make new friends. In a different school, there could be new magical traditions and spells for him to learn. He'd also face different challenges compared to Hogwarts.
She might have more time to explore the library on her own. Without the distraction of other students at first, she could discover some really rare and powerful magic books. This could give her a head start in her studies and she might even come across some ancient spells that could be useful later in her adventures at Hogwarts.
Well, they could meet younger versions of themselves and their friends. It would be really interesting to see how they interact. They might also try to give some hints or advice to their younger selves, but they have to be careful not to disrupt the timeline too much. And they could discover secrets that were long forgotten in the present time.