It's possible that she meets some dark wizards or witches who are not as bad as she initially thought. Through interacting with them, she realizes that the world is not simply divided into good and bad as Hogwarts often makes it seem. This could lead to a whole new perspective for Hermione in the fanfiction.
She might encounter some magical creatures that are not usually seen near Hogwarts. For example, a group of centaurs who have their own wisdom to share with her. Or she could come across a stray hippogriff that she befriends and it helps her on her journey.
She could meet other outcasts from the wizarding world. There might be witches and wizards who have left Hogwarts for similar reasons and they form a sort of community in hiding. Maybe she'll meet a powerful but reclusive wizard who can teach her things that Hogwarts never could.
Mal might meet a group of outcasts like herself. They are all running from different problems but have formed a kind of family. Together, they teach Mal the importance of community and support, and they all help each other face the challenges that come their way.
He could meet some of Iwa's powerful ninjas. Maybe Onoki, who could either see him as a threat or an opportunity. There might also be some young Iwa ninjas who are curious about Naruto and his abilities.
He might meet some of his distant Uzumaki relatives. There could be elders or other Uzumaki clan members who have valuable knowledge about his family and their special abilities.
He would surely meet Gaara. Gaara has had his own struggles and he might be able to understand Naruto on a deeper level. They could form an even stronger bond than before, with Gaara helping Naruto hide from those who might be looking for him in Suna.
He might meet some of the more reclusive characters in Ooo that we don't usually see in the show. Maybe a hermit - like wizard who gives him some cryptic advice.
He might meet American witches and wizards. Maybe a young and adventurous wizard who shows him around the American magical world.
It could be her best friend. In many stories, best friends have a special bond and can sense when something is wrong. So, her best friend might start looking for her and be the first to find her.
Akko might encounter a group of rebel witches. These witches have their own unique way of using magic, different from what she learned at Luna Nova. They might initially be suspicious of her but then become her friends and teach her their style of magic. They could also help her understand that there are many ways to be a witch, not just the way the school teaches.
Her friends would be extremely worried. Harry and Ron, especially, would be very concerned about her safety. They might start searching for her immediately, thinking that she could be in some kind of trouble or danger. They know Hermione well and understand that she wouldn't run away without a good reason.
Maybe she'll come across a group of traveling merchants. They would introduce her to different cultures and items she's never seen before. This encounter could open her eyes to a world beyond her village and influence her decision on whether to go back or not.