Well, in addition to Harry and Teddy, there might be some original characters created specifically for this fanfiction. For example, a local New York wizard who helps Harry and Teddy navigate the city's magical underbelly. Or perhaps a Muggle - born witch who is friends with them and provides a different perspective on the magical world in a big city like New York. But at the core, it's Harry and Teddy who drive the story forward.
Another plot might involve Teddy getting into some sort of trouble in New York, like accidentally using magic in front of Muggles, and Harry has to come to his rescue and figure out a way to cover it up without breaking the Statute of Secrecy. It could lead to a lot of adventures as they try to avoid the attention of the Magical Congress of the United States of America.
One challenge could be the Time - Turner rules. If they are using a Time - Turner, they need to be very careful not to break any of the laws regarding time travel. For example, they can't be seen by their past selves or make significant changes that would disrupt the future they come from. Another challenge is the danger of the time period they visit. If they go to a time when Voldemort was active, they are at great risk of being detected by Death Eaters.
There are also other characters like Matt Donovan who, despite being human, has a good heart and knowledge of the town. He could potentially be an ally in a different way, like providing information about the town's non - supernatural aspects. And then there's Alaric Saltzman, who has dealt with all kinds of strange things. His experience and wisdom could be valuable to Harry and Teddy.
In fanfiction, Harry might be protective of Teddy because Teddy is Remus and Tonks' son. Harry has a strong sense of loyalty and he may feel a great responsibility towards Teddy as he lost his parents. Also, Harry has his own experience of growing up without parents, so he doesn't want Teddy to go through any hardships alone.
There could be a character like Jake, a young wizard who grew up in the New York wizarding community. He could be very street - smart and know all the hidden alleys and secret magical places in New York. He would befriend Harry and help him navigate the new environment.
Luna Lovegood would be a great addition. Her unique perspective on magic could offer new insights to Teddy. Also, Ron could be included as Harry's best friend. His humorous and sometimes clumsy nature could add some light - hearted moments to the story.
One possible reason could be to protect Teddy. Maybe there are some threats in England that Harry wants to keep Teddy away from. For example, there could be some dark wizards or dangerous magical creatures that target Teddy for some reason.
Hermione and Ron would probably be there. They are Harry's best friends, so they might be like aunt and uncle to Teddy. They could help Harry out with raising Teddy, like Hermione giving educational advice.