There's a good chance he'd cross paths with the mages of the College of Winterhold. They could teach him new magic techniques, or he could share his own magical knowledge with them. He might also meet the Dark Brotherhood, a secretive assassins' guild, which would put him in a rather dangerous and morally ambiguous situation.
He could meet the Nords. They are a tough and hardy race, and Harry might learn a thing or two from them about survival in the harsh northern regions of Tamriel.
Well, he might encounter all sorts of magical creatures that are native to Tamriel. Maybe he'd get involved in the political struggles there, like the conflicts between different factions. He could also learn new forms of magic that are unique to that world.
In this fanfiction, the plot could center around Harry Potter arriving in Tamriel during a time of great unrest. He discovers that there are parallels between the magical hierarchies in Tamriel and Hogwarts. He could get involved in the political struggles of the various factions in Tamriel while also trying to find a way back home. Along the way, he might teach some of the Tamriel mages about some of the more advanced magic he learned at Hogwarts, like Patronus Charms, and in return, learn about Tamriel's unique magical artifacts and how to use them.
Hermione could be there. She would be eager to study the different magics and books in Tamriel. Her intelligence would help Harry navigate the new world.
He could meet his younger self, Anakin Skywalker. That would be a really interesting encounter. He might also meet Qui - Gon Jinn, who could sense the conflict within him. And there's a chance he'd cross paths with Yoda in his prime, which would lead to some intense confrontations or perhaps even unexpected alliances.
He could meet his younger self. This would be a really interesting encounter as he could either try to guide his younger self or be shocked at how different he was back then. Another possibility is meeting some of the ancient heroes that he only heard about before. For instance, he might come across Hercules and learn from him.
He could meet new professors. These professors would have their own teaching styles and areas of expertise. They might introduce Harry to different aspects of American magic that he has never encountered before.
He could meet a Japanese witch or wizard who becomes his best friend. This person could teach him all about Japanese magical traditions and how to navigate the Japanese wizarding world. For example, they might show him how to use a Japanese - style magic wand.
He could meet some powerful criminals. These could be people with unique and dangerous abilities that Naruto has never encountered before.
To survive in Azkaban, Harry would need to keep his mind active. He could recall all his happy memories to counter the Dementors. His knowledge of magic could also be useful. For example, he could try to create some protective spells around his cell. And he might get some unexpected help from the guards or other mysterious forces within the prison.
He could meet a famous wizard author who is signing books in Diagon Alley. This wizard could give Harry some valuable advice about his future.