His best friend Grover would surely visit him. Grover would bring some of Percy's favorite foods from Camp Half - Blood, like blue cookies. Annabeth would also be there. She'd probably be reading books on mythology, trying to find a way to help Percy get better faster.
Harry Potter could visit Snape in the hospital. Despite their past differences, Harry might feel a sense of obligation or curiosity. He could be there to finally have an honest conversation with Snape and perhaps gain a better understanding of his actions throughout the years.
His teammates, Sasuke and Sakura, would surely visit him. They are his closest comrades, and they would be worried about his condition.
Ino would most likely be there too. Since they have been friends since childhood, Ino would be worried about Sakura's condition. She might bring some flowers and stay by Sakura's bedside, chatting with her about their memories and the village.
His friends like Misty and Brock would probably visit him.
Hermione would surely visit. She'd be there with a stack of books, ready to help Harry catch up on his studies while he recovers. And Ron would be right beside her, probably with some treats from the Hogwarts kitchen.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
There's a chance that it could be a character from Percy's family. For example, a distant relative who has been corrupted by some dark magic. They might betray Percy for their own gain or because they are being controlled, and this betrayal could lead to Percy being killed.
He might encounter new demigods who are also on the run or hiding from the traditional demigod society. These could be demigods with different powers or backgrounds that Percy has never seen before.
Another possibility is that Percy has suffered some sort of mental trauma from his battles. He's having nightmares and flashbacks, and his friends think the mental hospital can help him. But once inside, he realizes that there are dark forces at work in the hospital. He has to use his demigod powers subtly to protect himself and the other patients from these unseen threats.
Annabeth Chase would most likely be one of his allies. She has always been by Percy's side, and she shares his sense of justice. If Percy decides to take on the gods, she would be there to support him with her intelligence and strategic thinking.