Well, Hermione is a strong - willed character. In Beacon Hills, this would serve her well. She would not be afraid to stand up to the powerful supernatural forces there. She could become a sort of mentor figure to the younger characters. She might teach them the value of knowledge and how to use it in the face of danger. Also, her magic could be a great asset in battles against the various threats that the town faces on a regular basis.
In Beacon Hills Institute fanfic, a frequently seen theme is academic competition. Students are often competing for top grades or positions in the institute. The theme of love and romance also exists, with characters falling in and out of love within the institute walls. Moreover, the theme of loyalty is important, as characters have to decide who they are loyal to, be it friends, groups, or the institute itself.
The plot could involve Hermione using her magical skills in the world of Beacon Hills. Maybe she helps the pack with some supernatural threats using spells and potions. For example, she could create a protection spell around the town to keep out certain dangerous creatures.
One possibility is that Harry's arrival in Beacon Hills shakes up the existing power dynamics. If there are different factions in Beacon Hills, like werewolves, hunters, etc., Harry could be an unexpected wildcard. He might form alliances with some while being a target for others. His magical abilities could either be a great asset or a cause for fear among the residents. For example, if there's a conflict between the werewolves and some dark force, Harry could use his magic to help the werewolves in ways they never expected, but this might also draw the attention of those who don't trust magic in the town.
The Nogitsune could also be a great antagonist. It thrives on chaos and mischief. Percy's presence and his powers would be something the Nogitsune would want to either corrupt or use for its own evil purposes. It could try to possess Percy or those around him to gain access to his demigod abilities.
One possible plotline could be Bella adjusting to the supernatural elements in Beacon Hills. Maybe she discovers the existence of werewolves and other creatures and has to learn to co - exist. Another could be her forming new friendships or even romances with the local characters.
One popular Beacon Hills Institute fanfic is 'The Secrets of Beacon Hills'. It delves deep into the hidden lore of the institute and has great character development. Another one is 'Beacon Hills Institute: New Beginnings' which focuses on new students arriving at the institute and the challenges they face. And 'Midnight at Beacon Hills Institute' offers a spooky take on the institute's after - hours activities.
One possible reason could be to protect his friends. Maybe he discovers a new threat that is specifically targeting him, and he decides to leave Beacon Hills to draw the danger away from those he loves. For example, in some fanfictions, a powerful and vengeful supernatural being might be after Stiles, and he believes that by leaving, he can keep his friends safe.
Well, he might get involved in the supernatural chaos of Beacon Hills. Maybe he'd team up with the local werewolves or other supernatural beings to fight against a common enemy. He could use his demigod powers in unique ways, like using his water control against a fire - based threat in Beacon Hills.
If Harry Potter goes to Beacon Hills, he'd probably be quite confused at first. The rules of the supernatural world there are different from the wizarding world. But then, he would start to adapt. Maybe he'd team up with Scott McCall. Harry's experience in fighting Voldemort would give him the courage and skills to face the threats in Beacon Hills, like the Dread Doctors or the Nogitsune.