Perhaps they get involved in the American wizarding politics. The political situation in the American wizarding world might be different from that in the UK. Harry and Hermione, with their experience from the fight against Voldemort, could contribute to solving some problems in the American wizarding community, like issues related to the secrecy of magic in a more urbanized and diverse American society.
In some fanfictions, they might go there to search for something. Maybe they are looking for a magical artifact hidden in Australia. It could be a powerful charm or a lost spellbook that could help them in their fight against the Dark forces.
Perhaps they discover a long - lost vault. It could be a vault that contains powerful artifacts or important secrets about the wizarding world. This discovery would likely put them in danger as various dark forces would be interested in getting their hands on whatever is in the vault.
They might encounter new magical creatures unique to America, like the Thunderbird. Harry could use his fame to make connections with American wizards, while Daphne might be fascinated by the different magical culture there.
Well, they might change some important events. For example, they could prevent certain tragedies from happening in the wizarding world. Maybe they'd save some characters who died in the original timeline.
In fanfiction, they might relive their old memories. They could visit their favorite spots like the library where Hermione used to study all the time. Maybe they would share their experiences after leaving Hogwarts with the new students.
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.
In fanfiction, they might initially face hostility from some at the Burrow. Since Harry and Draco have a history of enmity, the Weasleys might be suspicious of Draco. However, as the story progresses, they could gradually come to understand each other. For example, Draco might show a different side of himself, like his knowledge of certain magic that could be useful to the Weasleys. And Harry could act as a mediator between Draco and the others at the Burrow.
Well, they could change their own relationships. Perhaps Hermione would be able to help her younger self be more confident. Ron might stop himself from making some of the silly mistakes he made in the past. And Harry could get to know his parents better. They could also influence the development of magic in Hogwarts. For instance, introduce some new spells or magical concepts they learned in their original time.
Well, Harry leaving for America in fanfiction could lead to him trying to adapt to a new culture. He might struggle with the differences in magic use between the two countries. For example, the way spells are pronounced or the types of potions that are popular. He could also get involved in some sort of mystery that is unique to the American wizarding community.
There's a possibility that he'll face new challenges. It could be a place full of dark magic or dangerous creatures. Harry would have to use his wits and skills to overcome these challenges, and this could be a great opportunity for him to grow as a wizard.