Well, perhaps Percy could be a new student at Hogwarts. He might face challenges like making friends in a new and magical environment. Maybe he gets sorted into a house and has to learn to fit in with his new housemates. He could also discover some hidden secrets about Hogwarts that are not known to many.
He could be friends with Neville. Neville is kind - hearted and they might bond over their shared experiences of feeling a bit out of place at Hogwarts. Another friend could be Luna. She has an open - minded and unique personality, and she would likely accept Percy for who he is.
Percy going to Ilvermorny would be a wild ride. First, he'd be amazed by the castle itself. The four houses would be a new concept for him. He might be sorted into a house based on his heroic nature, like Thunderbird perhaps. He'd introduce the idea of Greek gods to the students there, which would cause quite a stir. And his relationship with Annabeth would be put to the test as they are separated by different magical institutions.
He might meet some talented witches and wizards. Maybe there would be a student who is an expert in magical beasts and they could share stories about their encounters with strange creatures.
There's a chance that Percy meets the personification of Tartarus itself. It could be a shadowy, all - powerful being that tries to break Percy's spirit. Percy, being the brave hero he is, would have to resist and find a way to either outwit or overpower this entity in order to continue his journey in Tartarus.
Perhaps Percy will meet a group of environmentalists. Given San Francisco's reputation for being environmentally conscious, they could be fighting against some sort of sea - related pollution that Percy gets involved in. He might use his powers and knowledge to assist them, and in the process, make some good friends.
He could meet some of the older campers who usually don't interact with the new arrivals right away. They might give him some special advice or warnings about the camp.