It's possible that there's a strange illness going around the village and Naruto goes to the hospital to see if he can offer any help. He has a strong sense of justice and would want to do whatever he can to stop the spread of the illness and make sure everyone gets better.
If you had ADHD, you could go to the departments of the pediatric-neurology department, the pediatric-psychiatric department, the pediatric-health department, the pediatric-rehabilitation department, the pediatric-neurology department, the psychopsychology department, the pediatric-development department, and so on. These departments had professional doctors who could diagnose and treat them. The specific department to choose could be decided according to the patient's specific condition and the division of departments in the hospital.
It could be that he was chasing an enemy or a valuable item that ended up in Hozukijou. Naruto is often on a mission to protect or retrieve something, and this place might be the destination of such a quest.
In fanfiction, Naruto could be driven to the library by his desire to understand the world outside of Konoha better. He has seen so much in his adventures, but there's still a lot he doesn't know. The library could have books about different lands, their cultures, and their forms of ninjutsu. By studying these, Naruto can become a more well - rounded ninja and gain a broader perspective on the ninja world as a whole.
In some fanfiction concepts, Naruto may go to Orochimaru for the sake of a friend. For instance, if a friend is dying and Orochimaru has the cure or a way to save that friend. Naruto is very loyal and would do almost anything for his friends. So, he might take the dangerous step of going to Orochimaru, even though he knows how dangerous and untrustworthy Orochimaru is.
One reason could be for guidance. Naruto often looks up to Kakashi and might need his advice on a difficult situation, like dealing with a new powerful enemy.
Maybe he got injured in a battle. That's a common reason for characters to end up in the hospital in comics.
They may be hiding because of a prophecy. There could be a prophecy that says Naruto and Temari together can change the fate of the ninja world in some way. But there are also forces that don't want this to happen. So, they hide to protect themselves until they can figure out how to fulfill the prophecy safely.
Maybe Clay was in the hospital due to an accident or a serious illness that was part of the fanfiction's plot.
Maybe he got into an accident or was seriously ill. That's a common plot device in such fanfictions.
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.