One possibility is that they go back to Hogwarts to teach. Ron could teach something related to magical creatures perhaps, using his experience from all the adventures. Hermione would be great at teaching Transfiguration or History of Magic. They could also start new clubs or improve the existing ones. And of course, there would be lots of interaction with other old friends who are still at Hogwarts or come back for a visit. Their relationship might also develop further in this familiar yet new environment.
Well, they could get involved in some sort of mystery at Hogwarts. Since they are quite experienced now, they might be the ones to solve it. For example, there could be a strange magical phenomenon in one of the secret passages, and they use their combined knowledge and skills to figure it out. They might also mentor some students who are having trouble with their studies or facing bullies, just like how they were once students there.
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.
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.
Maybe they miss their old school days. Hogwarts was such an important part of their lives.
In fanfiction, it could be a very awkward encounter. Ron might be shocked by the Dursleys' rudeness towards magic. He could be quite outspoken about it, which would make the situation tense. Hermione, on the other hand, would probably try to be more diplomatic. She might attempt to explain magic to the Dursleys in a calm and rational way, but they likely wouldn't listen.
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, Hermione's parents might be amazed by the magic all around. They could be shown the Great Hall and be astounded by the floating candles. Maybe they get to meet some of Hermione's friends like Harry and Ron, and have a friendly chat with Dumbledore who would explain the magical world to them.
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.
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.
Well, in many fanfictions, Hermione's parents might be initially a bit surprised by Ron and Harry's wizarding world ways. They could be impressed by their magical skills. Maybe Ron would make them laugh with his goofy charm, and Harry would seem very polite and brave to them.
She might discover a new side of the Weasley family. Since Ron's older brother is likely to have different experiences and skills compared to Ron, Hermione could learn a great deal from him. For instance, if he's more involved in magical research, he could share some of his findings with her.