Perhaps he would focus on his training and become a master of a new, unique form of jutsu. He might then open a dojo to teach the younger generation his skills, rather than aiming for the Hokage position. This way, he could still have a great influence on the ninja world.
Naruto could also choose to be a diplomat for Konoha. Since he has friends all over the world, he could use those relationships to strengthen bonds between different villages. This would be a significant role that doesn't require him to be Hokage. He would be like an ambassador, traveling between villages and promoting peace and cooperation.
One possibility could be that Naruto focuses more on his training to become a super powerful ninja without the burden of being Hokage. He could travel the world, learn new jutsus from different regions, and form alliances with various ninja clans on a more personal level rather than as a Hokage.
Shikamaru is another possibility. He is known for his strategic mind. As Hokage, he could use his intelligence to make wise decisions for the village. He may not have the brute strength of Naruto or Sasuke, but his ability to plan and analyze situations would be invaluable in leading Konoha.
One possible path is that Naruto becomes a traveling ninja, similar to Jiraiya. He could go around different villages and countries, learning new jutsus and making friends without the burden of leading a village. He might focus on spreading the message of peace in a more direct, personal way.
Perhaps the Hokage has made a decision that Naruto believes will destroy the village's future. Like if the Hokage decides to sacrifice a large number of innocent villagers in order to achieve a short - term goal. Naruto, with his strong sense of justice, might see killing the Hokage as the only way to stop this madness.
One possible storyline could be that Naruto decides to focus on traveling the world instead of becoming Hokage. He could use his skills to help people on a more individual basis across different villages. He might learn new jutsu from various shinobi cultures and become a sort of wandering hero.
Sasuke could also be a possibility for the 6th Hokage in the fanfic. He has grown stronger over the years and his unique perspective on the ninja world could bring new ideas to the leadership of the Hidden Leaf. He might start off as a controversial choice but prove himself through his actions in protecting the village and making tough decisions.
Sasuke could be an alternative. He has strong ninja skills and a deep understanding of the ninja world. His experiences have made him grow into a very capable person, and his Sharingan gives him an edge in combat and strategic planning.
One possible plot could be Naruto dealing with the boredom of retirement. He might try to find new hobbies like gardening in Konoha. Maybe he starts teaching some young ninja in an unofficial way, passing on his unique skills and experiences.
One possible plot could be Naruto facing the challenges of rebuilding the village after a major war. He'd have to deal with political intrigue from within the village, like some clans trying to gain more power. Also, he might focus on training the next generation of ninja to be stronger and more united.
The fanfic might focus on the 6th Hokage's personal growth. He could start off with insecurities but as the story progresses, he overcomes them through various trials. For example, he might have to deal with a powerful rogue ninja who challenges his authority. In the process, he discovers new powers within himself and also learns more about the history of the ninja world. This growth not only makes him a better leader but also a more respected figure among the ninja community.