They might go on an adventure together. Maybe they discover a hidden beach or a mysterious cave. They could also have some really deep conversations about their past experiences and their future plans.
One scenario could be that they compete in some local beach games. Percy would be great at water - related games, and Annabeth could use her strategic mind in other games like beach volleyball. Another could be that they get lost in a new town during their vacation and have to rely on each other's skills to find their way back.
In a fanfiction, they might meet in a dangerous, enchanted forest. Percy has been lost in there for days, and Annabeth has come to find him. As Percy hears the rustling of leaves, he gets ready to fight, but then he sees Annabeth emerge from the bushes. Annabeth quickly assesses the situation and starts leading Percy out of the forest, all while they catch up on what has happened since they last saw each other. There are strange creatures lurking around, but they feel safer now that they are together.
There could be a school janitor who is actually an old demigod who retired from the hero business. He could give Percy some valuable advice based on his own experiences. And of course, Percy will surely meet Annabeth's classmates, some of whom could be friendly and some not so much, depending on how they react to the new boy in school.
Grover could be one of Percy's friends to meet Annabeth. He's a satyr and has been with Percy through a lot. When he meets Annabeth, he might be really happy to see another important person in Percy's life.
One possible plot could be that Percy and Annabeth accidentally join the same online gaming group. They start off as rivals within the game, constantly trying to outdo each other in quests and challenges. But as they communicate more through the chat function, they start to realize they have a lot in common. They gradually become friends and start sharing their real - life problems. Eventually, they plan to meet in person at a gaming convention.
One possibility is that they meet by chance in a big city. Percy might be working as a marine biologist and Annabeth as an architect. They could initially not recognize each other due to the years apart. Then, as they start talking, the old memories and feelings start to resurface.
In fanfiction, when Percy and Annabeth meet, they might have a super sweet reunion. Maybe they'll share a warm hug and exchange some inside jokes that only they understand. It could be in a new and exciting setting, like on a mysterious island they've never been to before.
In many fanfictions, when Annabeth's friends meet Percy, there could be a mix of reactions. Some might be initially cautious, especially if they've heard of Percy's dangerous adventures. But often, they end up being impressed by his skills and his loyalty to Annabeth.
In fanfiction, they might first be a bit shocked to see each other. Then they could start reminiscing about their old adventures. Maybe they'll decide to team up again for some college - related mystery.