The setting of San Francisco can add a lot of mystery. With its foggy weather, it can be a great place for monsters to hide. Also, the city's many hills and old buildings can be like a maze for Percy to navigate, making it more exciting when he's on a quest.
One popular plotline could be Percy exploring the hidden magical spots in San Francisco. For example, he might discover an ancient Greek relic hidden beneath the Golden Gate Bridge. Another could be him facing off against new monsters that are drawn to the city's unique energy. Maybe there are sea - based monsters emerging from the San Francisco Bay.
Well, he might encounter new mythological creatures unique to the San Francisco area. Maybe there are sea monsters in the bay that he has to deal with, just like in his previous adventures but with a local twist.
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.
In fanfiction, Percy's move to San Francisco could bring new relationships. He could meet a girl who is also a demigod but has been hiding her identity. They start as friends but soon realize they have a special connection. Also, his relationship with his old friends might change. Some might visit him, and they have to adjust to the new environment together. He may also have new enemies. There could be a group of powerful witches in the city who see Percy as a threat to their plans of ruling the magical underworld of San Francisco.
Well, perhaps Percy goes to San Francisco to explore its famous landmarks like the Golden Gate Bridge. He might meet new friends or encounter some challenges specific to the city.
Perhaps there's a special event in San Francisco that Annabeth wants Percy to be a part of. It could be a celebration, a reunion of some sort, or an opportunity for them to have some time away from their usual troubles and just enjoy each other's company in a new and exciting city.
In the fanfiction, they could meet up with some of Annabeth's friends in San Francisco. Percy would probably be a bit out of place at first, but with Annabeth by his side, he'd soon warm up. They could end up having a great time at a local café, chatting and just enjoying each other's company while sipping on some coffee.
You can include the famous cable cars in San Francisco. Maybe the trainers use them to travel between different Pokemon gyms or areas where rare Pokemon are found. Also, the city's love for food can be part of it, like having Pokemon battles near famous food markets, and the winner gets a special local treat.