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.
There would be new students as well. Some of them could be descendants of the original founders of Ilvermorny. They might have stories and knowledge about the school's history that they could share with Harry. Also, he might meet students with unique magical talents, like those who are especially good at transfiguration or potion - making in a different way than at Hogwarts.
In some fanfictions, Harry might find it difficult to adjust to the new magical environment at Ilvermorny. The different houses, like Horned Serpent, Wampus, Thunderbird, and Pukwudgie, would be a new concept for him compared to Hogwarts' houses.
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.
He could meet the Dalton students. They might be very different from his Hogwarts friends, maybe more focused on academic magic in a different way.
He could meet an Egyptian wizard who is an expert in ancient magic. This wizard could teach Harry a great deal about the history of magic in Egypt.
There's a chance he'll meet other outcast wizards. These wizards might have been shunned by the wizarding world above ground. They could be very different from the wizards Harry is familiar with, perhaps having their own unique styles of magic. They might initially be hostile to Harry, seeing him as an outsider from the 'normal' wizarding world, but later they could become his allies. They might also know secrets about the underground world that could help Harry in his future battles or quests.
He might meet Canadian witches and wizards. There could be a friendly wizard who shows him around the Canadian wizarding community.
He might meet international aurors. These are highly skilled wizards from different countries who are experts in dark wizard catching. They could teach Harry some new combat spells.
He could meet Fleur Delacour's family. Since Fleur is from France, her family might be an important part of the French wizarding community that Harry interacts with.