Perhaps a story where the Beatles are brought to the future. They'd be shocked by the modern technology and music scene. They could then collaborate with modern musicians, creating a unique musical fusion. This would be a really exciting plot as it combines different musical eras.
One interesting plot could be a fan traveling back in time to attend a Beatles concert. They could interact with the band members, and maybe even influence their music in some small way.
A plot could involve time travel that causes a disruption in the Beatles' history. For example, a time - traveling character accidentally prevents John Lennon from meeting Paul McCartney. Then the story could be about how the character tries to fix this mistake and restore the Beatles' original timeline. This would involve a lot of research into the Beatles' early days and the relationships that led to their formation.
Maybe they travel back to the era of their early days but with the knowledge they have from their later success. They could use this knowledge to avoid some of the early mistakes and rise to stardom even faster. They might also introduce some of their later hits much earlier, changing the course of music history.
One idea could be Madara traveling back to the era of the Sage of Six Paths. He could try to change the very foundation of ninjutsu, which would create a whole new timeline. Maybe he would attempt to gain the power of the Sage for himself much earlier in history.
Well, perhaps a time - traveling device accidentally sends Judy Hopps back to a time when prey and predator relations were extremely tense. She has to use her wits and modern - day knowledge to prevent a major conflict that could have changed Zootopia's future for the worse. Or, a time - traveling fanfiction could focus on Nick Wilde going back to his own past, where he can make different choices that would impact his relationship with Judy and his standing in Zootopia society in the present.
One idea could be a character from the present in BO2 traveling back to a crucial moment in the game's history to change the outcome of a major battle. This would create a whole new timeline and a lot of interesting interactions with past characters.
Perhaps they travel forward in time instead. They could see the consequences of their actions in the future. Maybe they find out that their actions had unintended negative effects on some of their friends or the city as a whole. This would lead them to go back and try to fix things in a different way.
One idea could be Sauron travels back to the time before the forging of the Rings of Power. He could try to prevent the elves from ever having the knowledge to create such powerful items, thus changing the course of Middle - earth's history in his favor. Maybe he would target Celebrimbor directly, the elf - smith who was crucial in the creation of the rings.
In some narusasu time travel fanfiction, Naruto might go back to the time when Orochimaru was first targeting Sasuke. He could then use his skills and knowledge to keep Sasuke safe and away from Orochimaru's influence. A different plot could be Sasuke traveling to a time when Naruto was ostracized as a child and being the one to support Naruto, which would change their relationship dynamic from the start. Also, they could travel to a time during a major battle and use their combined future knowledge to turn the tides in their favor.
Another plot could involve Merlin traveling to the future. He might see a desolate Camelot, destroyed by some unknown force. Then he has to return to his own time and figure out how to prevent this dark future from happening. This would involve him using his magic in new and creative ways to influence the present to change the future.
One idea could be Sasori traveling back to his childhood and trying to change his path towards becoming a puppet. He might attempt to save his parents and avoid the tragedies that led him to his cold-hearted ways. Another plot could be Sasori traveling to a future where the Akatsuki has achieved its goals, only to find that the world is in a state he didn't expect, so he has to go back and change the Akatsuki's plans. Or he could travel to different ninja villages' pasts to steal their most powerful puppet - making secrets.
A possible plot for 'Haikyuu time travel fanfiction' is that Tsukishima travels back to his childhood when he first started to dislike volleyball. He could then understand why he developed that negative feeling and change his attitude from the start. This would lead to a much stronger Tsukishima in the present day. Another idea is that a team manager travels back in time to recruit a different set of players for the team, creating a completely different team dynamic. Maybe they could even bring back an old - school player who had unique skills that could revolutionize the team's playing style.