I think he might discover hidden powers within himself or learn unique jutsu from unexpected mentors. Maybe he'll even get involved in battles to protect the weak and uncover dark secrets along the way.
Well, he could encounter new allies and enemies in different villages and face all kinds of challenges on his own journey.
He might face new enemies and challenges outside Konoha, having to prove himself independently without the village's support.
Perhaps they are leaving together to search for a cure for some new and dangerous disease that has started to affect ninjas. They believe that by traveling the world, they will find rare herbs or meet wise sages who can help them develop a remedy. Naruto's determination and Hinata's knowledge of medicinal plants could be a great combination for this noble quest.
He might encounter unique and dangerous beasts in Uzushiogakure. Fanfiction often has new and exciting creatures for the protagonist to face, and Uzushiogakure's different environment could be home to such beasts.
They might have adventures in training Naruto to control the Nine - Tails' chakra better. Jiraiya could take Naruto to different secluded places where he can practice without distractions. Maybe they encounter strange and powerful beasts along the way, which Naruto has to learn to fight using his new skills.
His journey could lead him to the outskirts of the ninja world, to places that are unknown and full of mystery. With the Rinnegan, he might be able to access hidden paths or dimensions. He could be exploring these uncharted areas to gain more power and understanding, away from the politics and rules of Konoha.
One possibility could be that Naruto leaves Konoha and stumbles upon a village where everyone talks in rhymes. He tries to communicate but ends up making a comical mess of things. For example, when he asks for food, he says it all wrong and the villagers think he's performing a new kind of comedy act.
They could have adventures like learning new jutsus. Maybe they meet some of the famous ninjas in Konoha and get trained by them. They might also explore the unique places in Konoha, such as the Hokage Monument.
He might discover long - lost jutsu. Ancient ruins could hold scrolls with forgotten techniques that Naruto could learn and use to become even stronger in his ninja journey.
Another reason could be that he witnesses corruption or unfairness within the village leadership. If he sees that the system is rigged against certain groups, including himself or his friends, he could grow to hate Konoha and decide to leave.
He might go on adventures to protect his child from various threats. Maybe he travels to different hidden villages, facing new enemies and making new allies along the way. He could also be on a journey to discover more about his own family's past to better protect his child's future.