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.
Well, perhaps she could be a transfer student. She'd bring her combat skills from the Batman world to Hogwarts. Maybe she'd get into trouble for using non - magical ways to solve problems at first, like trying to physically fight a magical creature instead of using a spell. And she'd probably be really good at Defense Against the Dark Arts because of her training as a vigilante.
She could meet her younger self. This would be an interesting encounter as she could offer advice and guidance to her younger version. Maybe she could help her younger self to be less afraid of her powers.
One great Damian time travel fanfiction is 'Damian's Time - Twisted Adventure'. In this fic, Damian travels back in time and has to team up with a younger version of Batman to stop a threat that could change the entire timeline. It's full of action and really delves into Damian's character development.
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 could meet her younger self. It would be an interesting encounter as she could give advice to her younger version. Also, she might meet the earlier versions of her friends like Jiraiya and Orochimaru when they were all young and training together. Another possibility is that she could meet Hashirama Senju, the first Hokage, and learn from him directly about the founding of Konoha and his ideals.
She might meet her younger self. This could be a really strange encounter as she tries to understand how she used to be.
There's a possibility that Zuko would meet his grandfather. His grandfather's actions and decisions might have influenced the path the Fire Nation took towards war. By meeting him, Zuko could try to sway his grandfather's views and change the future of the Fire Nation at its root.
He could meet his past allies in a different context. For instance, he might encounter Kakyoin or Polnareff when they were just starting their journey. Maybe he could also run into Dio at a time when Dio was still plotting his rise to power, which would create a very tense situation.
She could also encounter characters who were once enemies but are now in a different situation due to the time travel. For instance, she might come across a young Death Eater who hasn't fully committed to the dark side yet. Ginny could try to change their path and prevent them from becoming evil in the future.