They might meet other famous wizards from around the world who are also in America for various reasons. For instance, they could run into a famous European wizard who has moved to America to start a business in the magical world, like a new type of magic potion shop. And this wizard could become their new friend or mentor in their new American life.
There could be young American witches and wizards at a magical school or gathering. Harry and Hermione could befriend them and learn about the social aspects of the American magical community. These young wizards might introduce them to new forms of magical entertainment or sports that are popular in America but not so well - known in Britain.
They could meet American wizards who have a very different style of magic. Maybe some of the native American wizards who have their own ancient magical traditions. These wizards could teach Harry and Hermione about magic that is connected to nature in ways they've never seen before in Britain.
They could meet new magical students at Ilvermorny. For example, a young and talented witch or wizard who is curious about their experiences at Hogwarts.
Perhaps he's following a lead related to his parents. There could be some secrets about his family that are hidden in America. He goes there to uncover the truth and learn more about his family's past that might not be available in the UK.
He could meet American witches and wizards. Maybe a friendly wizard who shows him around the American wizarding areas.
Perhaps she tries to find them right away. Using her intelligence and resourcefulness, she starts to search for any clues as to where they might have gone. She could ask other friends, like Neville or Luna, if they have seen Harry and Ron. And she might be determined to bring them back, not willing to give up on their friendship easily.
They could be on a mission to exchange magical knowledge. Hogwarts has its own set of spells and magical techniques, and so does the American wizarding world. They might go to America to learn new things and share their knowledge as well.
One reason could be to search for a powerful magical artifact outside of Hogwarts that they believe is crucial for defeating a new dark threat. In fanfiction, they might feel that Hogwarts has become too dangerous or restricted in terms of resources for their mission.
One reason could be to find peace. After all the chaos and war in England, they might just want to get away from it all and start fresh somewhere else.
One reason could be the media attention. After all they've been through, they might be tired of constantly being in the spotlight. The British wizarding press could be hounding them, so they leave to get some privacy.
He might cope by focusing on his training. Harry could see it as an opportunity to become stronger without distractions. He would pour all his energy into learning new spells and improving his magical abilities.
Harry might meet some American wizarding families that have long - standing traditions different from the pure - blood families in the UK. These families could introduce Harry to new forms of magic and social norms within the American wizarding community. He could also meet American Muggle - born wizards who have their own unique stories of discovering magic in a different cultural context compared to what he's used to.