Definitely Jaime Lannister. His character had a lot of development in the original series. If reincarnated, he could either redeem himself even further or take a completely different path. He might try to make amends for his past actions by becoming a true knight, or he could turn against his family if he realizes the toxicity of their ways. His reincarnation would bring a whole new set of possibilities to the story.
Reincarnating as Tyrion Lannister would be really interesting. He's already a complex character with a sharp mind. As someone reincarnated, you could use your modern ideas to enhance his political acumen even more. You could also try to change his relationship with his family for the better, or at least make his life less miserable while still being the clever dwarf everyone fears and respects in the political arena.
Cersei could be the most interesting in a sense. If she were reincarnated, she could either double down on her power - hungry ways or completely change. Maybe she could learn from her past mistakes and become a more benevolent ruler. Or she could use her reincarnation as a way to exact revenge on those who opposed her in her previous life in more devious and calculated ways.
Reincarnating as Carlisle Cullen could be interesting. You could explore his past more deeply and maybe change some of his decisions regarding the vampire lifestyle. Another option would be to reincarnate as Rosalie Hale. You could show her softer side and how she copes with her past traumas in a different way.
I think being reincarnated as Loki would be super interesting. He's such a complex character with his own motives and schemes. You could take over Loki's life at a certain point and use your modern - day knowledge to either further his plans in a different way or completely change his path. Maybe you could prevent him from getting into so much trouble with Thor and the Avengers, or use his shapeshifting abilities in ways that no one in the Marvel universe has ever seen before.
I think Daenerys Targaryen would be really interesting. If she were reincarnated, she could use her past experiences to be an even more powerful and just ruler. She already had a complex journey in the original series, and reincarnation would add more depth to her character. She might be able to avoid some of the mistakes she made in her first life, like trusting the wrong people.
I think Bran Stark could be very interesting too. As the Three - Eyed Raven, he has vast knowledge and powers. In a future fanfic, he could use his powers to foresee and prevent new disasters or to guide the future of Westeros in a more positive direction. However, his new powers might also make him a target for those who fear his influence.
Being reincarnated into Master Roshi would be an unexpected but fascinating choice. With the knowledge of modern times, the reincarnated person could introduce new training techniques to Goku and Krillin from the very beginning. They could also use Roshi's pervy side in a more comical way to create some light - hearted moments while still being a respected martial arts master.
I think Tyrion would still be really interesting. He's so clever and adaptable. In a modern setting, he could be a brilliant strategist in business or politics, using his wits to outmaneuver his opponents just like he did in the show.
Daenerys Targaryen would also be a top candidate. Her quest for the Iron Throne and her connection with her dragons. When she meets the demigods, she might see them as either threats or potential allies. Her experience with magic and her strong will would make for some intense interactions with the Percy Jackson characters, especially when it comes to issues of power and leadership.
Jon Snow would be an interesting character in a 'Game of Thrones' and 'Harry Potter' crossover. He has a strong sense of duty and honor, similar to some of the characters in Harry Potter. He could be introduced to the concept of magic and might be skeptical at first. But as he sees the power of magic, he could use it to better protect the North. He could also learn from the wizards about different ways of leadership. And his relationship with the direwolves could be explored in new ways, especially if there was some sort of magical connection between them and the magical creatures in Harry Potter's world.