One interesting plot could be that Harry accidentally travels back to the time when his parents were at Hogwarts. He gets to see them in their youth, and maybe even interacts with them in a way that doesn't disrupt the timeline too much. For example, he could help his father with a prank that was a big part of his father's Hogwarts story.
Another plot might involve Hermione. Suppose she accidentally travels back in time. She could use her vast knowledge to solve some mysteries that were left unsolved in the past at Hogwarts. She might find out the real origin of a particular magical artifact or spell that was lost in history. This could change the way they view certain aspects of magic in the present time.
Some fanfictions might have a scenario where an accidental marriage occurs between a Hogwarts student and a Death Eater's child. This creates a huge conflict not only between the two individuals but also between their respective groups. For instance, if Draco's sister was accidentally married to Neville. They would have to face the prejudices from both sides, and also try to find a way to either end the marriage or prove that love can overcome the differences in their backgrounds.
A plot could be that James Potter travels back to the time when Voldemort was still Tom Riddle at Hogwarts. He could try to influence Riddle in a positive way, perhaps by befriending him and showing him a different path than the dark one. However, he has to be careful not to change the future too much or risk endangering his own existence and that of his family.
One interesting plot could be a character going back in time to prevent Voldemort's first rise to power. They could try to change the events that led to his initial gathering of followers. Another plot might involve a time - traveling student who accidentally alters the sorting of the houses, causing chaos and new alliances within Hogwarts. And a third could be a time traveler going back to the Marauders' era and getting involved in their pranks and adventures, which in turn has unforeseen consequences for the future.
One interesting plot could be the characters going back in time to prevent certain dark magic events from ever happening. For example, they might stop Voldemort's rise to power much earlier in history.
A possible plot is that Harry travels back to a time when the Marauders were in school. He could become friends with them and try to prevent some of the bad things that happened to them later. He could also use his knowledge of the future to help them in their pranks and adventures. This would be really interesting as he would be interacting with his father and his friends in a whole new way. It could also lead to changes in the future relationships and events at Hogwarts.
A cool plot in a smart Harry Potter time travel fanfiction could be that Harry travels back to the time when the Marauders were at Hogwarts. He could join their group and influence their actions in a positive way. Maybe he could prevent Sirius from being framed. Or, he could go back to the Triwizard Tournament time and figure out a way to expose Barty Crouch Jr. much earlier. Also, he might travel back to the time of the Goblin Rebellions and learn about the true relationship between wizards and goblins, which could change how he views things in his own time.
Hermione is also a prime candidate. Her inquisitive nature and her thirst for knowledge could lead her to accidentally stumble upon a time - traveling mechanism. Once in the past, she could use her intelligence to interact with historical figures and gain new insights into magic that she could bring back to the present.
In some fanfictions, there could be a time - loop situation. Harry and Tom Riddle keep repeating a certain period of time, and each time they interact, they learn something new about each other. For example, they might start off as enemies but gradually come to understand the reasons behind each other's actions as they repeat the time period over and over again.
One interesting plot could be Lily traveling back in time to prevent James and Sirius from playing a particularly dangerous prank that had unforeseen consequences. Another might be Harry traveling back to meet his mother as a young witch and getting to know her in a whole new way. And perhaps Lily and Harry traveling back together to change certain events that led to the rise of Voldemort, like preventing the first opening of the Chamber of Secrets.
One interesting plot could be a time - traveling character going back to Tom Riddle's school days at Hogwarts. They might try to prevent him from becoming Voldemort. For example, they could befriend young Tom and show him a different path of magic, one that's more about using it for good and building relationships. This could change the entire future of the wizarding world.