One reason could be to search for a particular magical item. Maybe Dumbledore left behind a clue that led them to believe there was something important in one of the vaults at Gringotts.
Another possibility is that they suspect Gringotts is involved in some dark plot. So, they go there to investigate and find evidence. They might have overheard some suspicious conversations or received some cryptic messages that pointed them towards Gringotts.
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.
Often, the goblins can be antagonists. If they have their own motives that conflict with Harry and Hermione's, like protecting a dark secret in the vaults or trying to take advantage of the situation for their own gain. Another possible antagonist could be a Death Eater who has infiltrated Gringotts to either steal something important or to ambush Harry and Hermione.
It might be related to Hermione's research. She may have read about some unique magical phenomenon in Australia that she wants to study first - hand. And Harry, being her loyal friend, goes along with her. For example, there could be a special type of plant with healing properties that only grows in certain parts of Australia.
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 interesting plotline could be Harry and Hermione discovering a long - lost secret vault in Gringotts. Maybe it contains powerful magical artifacts that can change the course of the wizarding war. Another could be that they are on a mission to retrieve something from the vault that is crucial for their fight against Voldemort, like a spellbook with ancient and powerful spells.
It could be for safety reasons. If there's a threat at Hogwarts or in the wizarding world in general, Hermione's house might be a safe haven. Her family might have some protective spells around the house that Harry can take advantage of. Also, Hermione's parents are Muggles, so it might be a place where the dark forces wouldn't expect them to hide.
Maybe they miss their old school days. Hogwarts was such an important part of their lives.
Because it can rewrite the story. Fanfiction allows authors to take the basic setting of Harry going to Gringotts and turn it into something completely different. For instance, they can make it so that instead of just retrieving money, he is on a quest to find a magical key that unlocks a powerful spell.
Hermione might also come across some magical creatures that are guarding certain vaults in Gringotts. For example, a dragon that she has to find a way to bypass without getting burned. These encounters would add more excitement and danger to her visit to the wizarding bank.
It could be due to Harry's own charm and good nature. He's polite and respectful to Hermione's parents, and they can see his kind heart. Also, given his difficult background with his own family, Hermione's parents might feel a sense of compassion for him and want to provide him with the love and support he lacks from his own relatives.