Percy might run into his old friends' ancestors. This could create some really strange and exciting interactions. For instance, if he meets an ancestor of Annabeth, he could learn things about her family history that she doesn't even know.
Well, Percy could end up changing the entire course of history in the 'Percy is thrown back in time' fanfiction. He might accidentally stop some important relationships from forming or start new ones that were never meant to be. Also, he could have a chance to see his loved ones who are no longer alive in his original time, which would be an emotional rollercoaster for him.
He could meet his younger self. This would be a really interesting encounter as he could either try to guide his younger self or be shocked at how different he was back then. Another possibility is meeting some of the ancient heroes that he only heard about before. For instance, he might come across Hercules and learn from him.
He might meet his former classmates who have changed a lot since he left. Maybe some new students who are intrigued by his reputation.
He could meet his old teachers again. They might be surprised to see him back after his long absence.
He could meet his future self. This encounter might be full of surprises as his future self could have different views and experiences. His future self might be more jaded or more powerful.
He could meet an old wizard who has been guarding the vault for centuries. This wizard could either be a friend or a foe, depending on Percy's actions.
The Titans that were banished to Tartarus could be major antagonists. They might see Percy as an intruder and a threat, and try to stop him from escaping or even try to use him for their own purposes. Also, the various monstrous creatures native to Tartarus, like the Empousai or the Arai, could constantly be attacking Percy.
There's a good chance he'll meet the goddess Athena. Since Percy has a connection to the world of the gods, and Athena is known for her wisdom and strategic thinking, she could offer Percy some valuable advice. Maybe she'd help him navigate the complex social and political situations in ancient Greece or teach him some new ways to use his demigod powers.
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.