I think Tyrion Lannister would be an interesting character to time travel in a fanfiction. He's very intelligent and cunning. Time travel could be his way to outwit his family and those who have wronged him. Arya Stark could also be a likely character. She has the skills of a faceless man. If she could time travel, she could use her skills to change the past, perhaps by assassinating key enemies before they cause harm. And of course, Melisandre. She has some sort of magic related to seeing the future. It's not a stretch to think she could find a way to time travel in a fanfiction and change the course of events in Westeros.
Bran Stark is a popular choice too. Since he has the power of the Three - Eyed Raven, time travel can be related to his abilities. Fanfictions might have him traveling through time to gain more knowledge or to influence events in a more direct way. Jaime Lannister also features often. His character arc can be completely transformed through time travel, for example, going back to redo his actions as the Kingslayer or forward to see if he can redeem himself in a new Westeros.
Time travel in a Game of Thrones fanfiction can have a huge impact on the storyline. If a character travels forward in time, they could bring back knowledge of future events and try to prevent disasters. Or if they travel back, they might accidentally change things that were meant to happen. This could lead to different characters rising to power or falling from grace. For example, if a time traveler influenced Tyrion's trial, the outcome could change his entire future and the future of the Lannisters.
Batman himself is a likely candidate. Given his intelligence and determination, he might stumble upon a time - traveling device or technology while investigating some strange phenomenon. He would be driven by his need to protect Gotham, perhaps by preventing a future catastrophe that he has foreseen.
Ban could be another one. He has his own backstory related to the sins and his immortality. He might time travel to find a way to break free from his immortality curse or to go back and correct a mistake he made when he was under the influence of one of the sins, like greed when he stole something important in the past.
Star - Lord is a likely candidate. He's always been a bit of a risk - taker and his curiosity might lead him to experiment with time travel technology.
I think Fundy would be likely to time travel. He has a complex relationship with his family and the SMP. Time travel could be a means for him to understand his father better or change the way his family relationships developed. GeorgeNotFound could also be a candidate. He's often in the background but has a strong connection to Dream. Time travel might be his way of getting more involved in the SMP's events and helping Dream in a different way. Lastly, Niki could be a time traveler. She has been through a lot of changes on the SMP, and time travel could be her opportunity to go back and make the SMP a more inclusive and friendly place from the start, especially for those who have been marginalized.
Jon Snow would be a fascinating time traveler. He has a mysterious past himself, and going back in time could help him discover more about his true identity. He could also influence the events that led to the creation of the Night's Watch. Additionally, Cersei Lannister as a time traveler would be quite a story. She could try to rewrite her own history, or perhaps find a way to gain more power in a different time period, which would create all sorts of new power dynamics and conflicts in the story.
Well, Arya Stark has a good chance. She's highly adaptable and has been through so much. Her skills as a Faceless Man could potentially be used to discover the secrets of the time loop and break it. Also, Jon Snow. He has a special connection to the North and has faced death and come back. His unique position and the respect he commands could help him find a way to end the time loop. And then there's Tyrion Lannister. His intelligence and ability to think outside the box might lead him to the solution to break the loop.
A really creative plot is when a character from the modern world time - travels into 'Game of Thrones'. For example, in some fanfictions, a history buff suddenly finds themselves in the middle of Westeros. They use their knowledge of the series to try and prevent some of the more tragic events. It's a fun take on the time travel concept as they struggle to fit into the world and also make a difference.
Shinji is a very likely character. His complex relationship with his father and his role as the main pilot make him a prime candidate for time travel scenarios. He could go back in time to try and fix things or understand his father better.