Well, they could time travel to the time of the founders of Hogwarts. Teddy, with his unique abilities as a Metamorphmagus, could disguise himself and Harry to blend in. They could witness the four founders' relationships, how they chose the location for Hogwarts, and how they decided on the houses. This knowledge could then be used to better understand the current state of Hogwarts and maybe even solve some of the modern - day problems within the school like the ongoing house rivalries.
A great plot might be that Teddy time travels to a time when Harry was a child living with the Dursleys. Teddy could try to secretly protect Harry from some of the bullying and neglect he endured. Or perhaps Harry and Teddy travel to a time long before Hogwarts was founded to learn about the origins of magic in the wizarding world, and they bring that knowledge back to their own time to help improve modern magic.
They could time - travel to a time in Hogwarts' history when a great mystery was unsolved. Harry and Teddy could work together to figure out what really happened. For example, they might explore the mystery of the Chamber of Secrets long before Harry's own encounter with it. Teddy's inquisitive nature and Harry's experience could lead them to some amazing discoveries.
A possible plot in the Harry Potter Teddy time travel fanfiction could be Teddy going back to the time of the founders of Hogwarts. He could be a sort of mediator between the four founders, especially if there were some disputes or misunderstandings that led to future problems in Hogwarts. Teddy could use his knowledge from the future to try and smooth things over. This would not only change the history of Hogwarts but also have a big impact on the future wizarding world he comes from.
A third idea might be that both Harry and Teddy accidentally travel to a time in the past where a great magical event took place, like the founding of Hogwarts. They have to figure out how to get back to their own time while also trying not to disrupt the events that are crucial to the wizarding world's history. They might even learn some long - lost spells or magical knowledge during their time there.
One idea could be Teddy time - traveling back to the time when Harry's parents were alive. He could try to prevent their deaths, which would create a whole new timeline. Harry would then have a very different life, perhaps growing up with his parents and without the burden of being 'the boy who lived'.
One plot idea could be that Hermione and baby Teddy travel back to the time of the founders of Hogwarts. There, Hermione uses her knowledge to help the founders with some magical problems they are facing, while Teddy, being a metamorphmagus, unknowingly reveals some future magical abilities to the wizards of that time, causing a stir. Another idea is that they travel to a time during Voldemort's first rise to power. Hermione tries to find a way to stop him earlier, with Teddy's unique abilities helping them to blend in and gather information. For example, Teddy could change his appearance to look like a Death Eater's child to get close to their secrets.
One idea could be that Baby Teddy Lupin time - travels back to the Marauder era. He could meet his father, Remus Lupin, as a young boy. This would create some really heartwarming and bittersweet moments as Teddy gets to see his father's early life and perhaps even influence some events in a positive way.
Perhaps Teddy gets into trouble at Hogwarts, and Harry and Ginny have to step in to sort things out. It could involve Teddy being wrongly accused of something, and they use their skills and influence to clear his name. Or Teddy discovers a secret room in Hogwarts that only he can access, and he enlists Harry and Ginny to explore it with him.
Another idea is that they travel to a time just after the end of the First Wizarding War. There is chaos and rebuilding going on. Harry and Teddy could be on a mission to retrieve a powerful magical artifact that was lost during the war. Along the way, they meet survivors of the war and learn about the true cost of the conflict. Teddy, who has grown up in a post - Voldemort world, is deeply affected by the stories of those who lived through the dark times.
One interesting plot could be that Harry, Ginny and Teddy travel back to the time when the Marauders were at Hogwarts. They could interact with James, Sirius, Remus and Peter, and maybe even change some small events that have a big impact later. For example, they could prevent Peter from becoming a Death Eater spy, which would change the course of the war against Voldemort.
Well, perhaps in the fanfiction, Harry has to deal with the challenges of being a single father to Teddy. He might struggle with balancing his work at the Ministry and taking care of Teddy, which could lead to some really heart - warming and also tense moments. For example, he has to miss an important Ministry meeting because Teddy is sick.