Perhaps he would befriend the outcasts at Nevermore. The ones who are different from the rest and understand what it's like to be in a new and strange place.
If Harry Potter were to go to Nevermore Academy in fanfiction, his friends could be those students who share his sense of justice. There might be students who are also trying to make the academy a better place. Or he could become friends with students who are interested in his Hogwarts stories and magic. They would be intrigued by his experiences and the different kind of magic he knows. Also, students who have a kind heart and are not quick to judge him based on his being from a different magical world could become his friends.
Well, he might find the whole atmosphere very different from Hogwarts. He could meet new and strange characters with unique abilities. Maybe he would struggle to adapt to the different curriculum and social norms at Nevermore.
Hermione would probably be worried at first but then start researching all she can about space magic. Ron would be a bit more skeptical but also excited for Harry. They might try to find a way to communicate with him while he's in space, using some sort of enchanted device.
His other friends from Hogwarts might not even believe it at first. They might think it's some kind of elaborate prank. But once they realized it was real, they might try to find a magical way to communicate with him in Skyrim, or even try to open a portal to bring him back.
Harry Potter's sense of strategy would improve. Duel Academy has its own set of rules and strategies for dueling. He'd have to learn and adapt to them, which would make him a more strategic wizard. He'd also become more open - minded as he experiences a different magical education system. He might start to question some of the things he learned at Hogwarts and find new ways of thinking about magic.
Hermione would probably be a bit worried at first. She might think it's a waste of time compared to studying magic. But then she'd see the benefits of physical fitness and start to support him. Ron, on the other hand, would probably make fun of him a little but also be secretly impressed.
If Harry Potter goes to Kuoh Academy, he'd bring his own brand of heroism. He'd likely make friends quickly as he's used to facing challenges and helping others. His magic skills could be both an advantage and a source of mystery. The students at Kuoh might be intrigued by his spells like the Patronus Charm, which could come in handy in the different scenarios at the academy.
When Harry Potter goes to McKinley in fanfiction, he'd likely meet the jocks and the nerds alike. The jocks might be initially intimidated by his differentness, while the nerds would be fascinated and want to pick his brain about all things magic. He could also meet the school outcasts, who would find a kindred spirit in him.
Well, aside from Thor and Odin, he could meet Sif. Sif is a strong Asgardian warrior, and she might be interested in Harry's unique brand of magic. And of course, there's a high chance of meeting Loki. Loki is always up to something, and his devious nature could either make him an adversary or an unexpected ally to Harry.
He would most likely meet Peter Pan. Peter is the main character in Neverland and he would surely cross paths with Harry. Also, he might meet Tinker Bell, the feisty fairy. And of course, the Lost Boys would be there too, and they would probably be curious about this new boy with strange magical powers.
Hermione would probably be a bit worried at first. She'd be concerned about him missing out on important magical studies during the summer. But she'd also encourage him to have some normal, non - magical experiences. Ron, on the other hand, would be jealous. He'd wish he could go to a muggle summer camp too and experience something different. He might even ask Harry to bring him back some muggle treats.