There could be a secret passageway in the school that leads to an ancient mythological place. Percy and Annabeth discover it by accident. Percy is excited to explore but Annabeth warns him to be cautious. They enter together, facing various traps and puzzles inside. Along the way, they might meet some minor gods or spirits who are either helpful or try to hinder their progress. This adventure would test their skills and teamwork, just like their quests in the original stories.
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.
They could be involved in a high school project that turns out to be related to an ancient prophecy. Percy might use his water - controlling abilities in a science experiment in a really cool and unexpected way, and Annabeth would be there to explain the historical context behind it all.
Perhaps they meet a group of outcasts who have their own unique abilities. These outcasts could teach Percy and Annabeth new fighting techniques or ways to use their powers more effectively. They might join forces with them to take on a common enemy that is threatening both the outcasts and the world they come from.
They could have had an adventure in the school library. The library had a restricted section that was said to be haunted. Percy and Annabeth, being the curious ones, decided to check it out. They found an old book that seemed to have some strange power. As they opened it, they felt a gust of wind and strange symbols started to glow. They quickly realized they had to put the book back and figure out how to seal the power within it later.
They could have all sorts of adventures. Maybe they'd get sorted into different houses and have to deal with the rivalries that come with that. Percy might use his water - controlling abilities in the Hogwarts' lake, and Thalia could use her lightning powers during a stormy Quidditch match. Nico could explore the Hogwarts' underground secrets, using his underworld - related skills to uncover hidden chambers.
Percy might be a source of comfort for Annabeth. School can be a tough place sometimes, with all the academic pressure and social drama. Percy is someone she can always rely on, and without him, she feels less secure. Maybe he has a unique way of making her laugh or feel better when she's down, and she misses that a great deal.
He might meet normal high school students. There could be the typical jocks, nerds, and popular kids. Maybe he'd encounter a really smart student who is intrigued by Percy's different way of thinking. Or he could meet some mean students who pick on him at first but then learn to respect him.
In the fanfiction, they could also be on a quest to retrieve a powerful ancient Greek artifact. This artifact could be something like the Helm of Darkness that has been lost for centuries. Along the way, they would face many challenges. They would have to interact with the gods and goddesses of Ancient Greece, who might not all be friendly. Percy and Annabeth would rely on their friendship and unique skills to overcome all the obstacles in their path.
They might face new and strange monsters. For example, they could encounter a sea - serpent that has the power to control the weather around the Argo 2. Percy would use his water - controlling abilities to try and fend it off while Annabeth comes up with a strategic plan to defeat it.
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.