If Percy and Annabeth were to go to highschool in fanfiction, it would be a whole new world for them. They are used to the dangerous and magical world of demigods. At highschool, Percy might get into trouble for his impulsive nature, but his loyalty to his friends would also make him popular. Annabeth would be the girl who always has her nose in a book, yet she'd also be the one everyone turns to for advice. Their relationship would also develop in new ways, perhaps facing challenges from normal high school romances or jealous classmates.
Their relationship could become more complex. In highschool, there would be more social pressures. They might have to deal with classmates who are interested in one of them romantically, which could cause some jealousy. But it could also strengthen their bond as they face these new challenges together.
If Percy and Annabeth go to Hogwarts in fanfiction, it could be a wild adventure. Percy would likely be shocked by the lack of demigod - specific threats at Hogwarts. He might try to use his powers in the wrong way, like using his water powers to clean the Great Hall. Annabeth would be busy exploring the library and trying to figure out how the magic in Hogwarts works compared to Greek magic. They could end up teaming with Harry Potter and his friends to face a new kind of threat that combines the worlds of Greek mythology and Hogwarts magic.
They might face new challenges like dealing with difficult professors. In college, the academic pressure could be a big deal for them. Percy might struggle with some theoretical subjects, while Annabeth could thrive. And they could also encounter new mythological creatures that are lurking around the college campus.
Well, one possible plot could be Percy and Nico having to deal with typical high school problems like bullies. Percy might use his water powers in a discreet way to stop them. Nico could be the mysterious loner at first but then make some real friends as he shows his cool powers. And they might also have to hide their demigod identities from the normal students.
Percy might become friends with the misfits or outcasts at school. His kind heart and sense of justice would draw him to those who are bullied. Annabeth, on the other hand, could be respected by the smart kids for her intelligence. She might form study groups and in the process, make new friends. But some students might be jealous of their closeness and the special bond they share.
In a fanfiction where they go to high school, Percy would likely be popular for his heroic deeds and good looks. He might join the swim team and break all the records. Thalia could be the cool girl who rides a motorcycle to school and gets into trouble for parking it in the wrong place. Nico would be the mysterious new kid. There could be a plot where they have to team up to stop a monster that is lurking in the school basement.
A powerful monster from the demigod world that has a vendetta against Percy and Nico could be the main antagonist. It disguises itself as a teacher or a student and slowly starts to manipulate things in the school. It tries to isolate Percy and Nico from their friends and then attack them when they are at their weakest.
Her adventures could start right in her own backyard, so to speak. She might discover a hidden entrance to an ancient labyrinth in her neighborhood. As she explores it, she has to use her wits and any powers she has. Later, she could be drawn into a larger adventure where she has to stop an evil force from awakening an ancient and powerful Titan. She would travel across the country, or even across different continents in the demigod world, encountering various mythical beings. Some might be friendly and offer her help, while others would try to stop her at all costs. And through all these adventures, she would grow in strength and wisdom, just like her parents did before her.