He might meet a younger version of Alfred. Alfred has always been an important figure in the Wayne family and Damian could learn a lot from him, or even try to give him some hints about the future. Also, he could run into a younger Commissioner Gordon. Their interactions could be really interesting as Gordon is such an important ally of Batman.
Damian could meet his own grandfather, Thomas Wayne. This would be a very emotional encounter as Damian would be seeing a part of his family history that he only knew from stories. He might also meet some of the early rogues in Gotham. For example, he could come across a young Penguin or Riddler before they became the full - fledged villains he knew in his time. It would be a chance for him to try and stop their descent into villainy.
Well, one possibility could be that Damian Wayne goes back in time to prevent the death of his father, Bruce Wayne. He might use his skills and knowledge from the future to change key events that led to that tragic outcome. Maybe he teams up with a younger version of his father and other allies he knew from his own time, like Nightwing or Batgirl, to take on enemies that were too powerful in the past but not so much with his future knowledge and abilities.
He might meet Luke before he turned bad. Percy could try to change Luke's fate, convince him not to follow Kronos. It would be a great chance to save a friend and prevent a lot of the chaos that happened later.
In the 'Sora Goes Back in Time' fanfiction, Sora may run into his friends at different points in their lives. He could meet Riku when they were just kids, and see how their friendship started in a whole new light. He might also come across Kairi at a crucial moment in her past, and his presence could change the way she develops as a character. There could also be encounters with other minor characters from the original story, whose roles could be expanded upon in this time - traveling scenario.
Goku might run into past versions of his friends. He could see a younger Krillin or Bulma and have some really interesting interactions. He could also meet past versions of his enemies and try to change their fates. For instance, he could meet a young Vegeta and try to steer him away from the path of evil. This would be a huge change in the Saiyan's story.
She might meet her younger self. This could be a really strange encounter as she tries to understand how she used to be.
He could also meet some minor nymphs or spirits that inhabit the island. These beings might be curious about Percy's return and have their own stories to tell. For instance, there could be a water nymph who has some knowledge about a prophecy related to Percy and his return to Ogygia. Or a spirit that has been observing the changes in Ogygia since Percy last left and can give him some insights on what has been going on in his absence.
He could meet Dr. Halsey when she was just starting her research on the Spartan program. Master Chief could give her some insights from the future, which might change the way the program is developed.
Bella could meet an old neighbor. This neighbor might tell her about the changes in the neighborhood over the years. Maybe there are new families, new stores, or even some interesting local events that she has missed. It would be a great way to bring a sense of familiarity and newness to the story at the same time.
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.