At first, it might be a bit awkward as they are used to being in a group in Konoha. But as they face challenges together, like fighting off bandits or surviving in harsh environments, they would start to depend on each other more. This would lead to a deeper friendship. Sakura might start to see Naruto not just as the goofy kid she knew but as a reliable partner, and Naruto would see Sakura as more than just a friend who has a crush on Sasuke. Their relationship would evolve into a more equal and mutual respect - based one.
One reason could be to seek greater power. Maybe they feel that Konoha no longer offers the training or resources they need to reach their full potential. So they decide to leave and explore other places where they can become stronger.
Another reason might be that Naruto is seeking a greater purpose. In the fanfiction, his 'godlike' state could make him realize that there are threats out there that he can't face while being tied to Konoha. He may leave to protect the world on a larger scale, believing that he can be more effective away from the village.
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.
Some in the village would be sad to see them go. Naruto is a hero to many, and Hinata is also well - liked. People like Iruka would miss Naruto a great deal. But others might understand their need for a new life away from the village and support their decision.
One possible plot could be that they leave to find a new way to strengthen Konoha. Maybe they've heard of a powerful jutsu or artifact outside the village that could enhance the village's defenses. They journey together, facing various challenges like difficult terrains and enemy ninja along the way. During their travels, they might also have deep conversations, strengthening their bond as friends and comrades.
She might leave to find herself. In Konoha, she has always been defined by her relationships with Naruto and Sasuke. Leaving gives her the chance to figure out who she is on her own terms, away from the expectations of her friends and the village.
One reason could be to seek a new life away from the constraints of Konoha. Maybe they feel that they can't fully grow or explore their potential within the village. Another reason might be to protect Konoha in their own way. They could believe that leaving and dealing with threats from the outside would keep the village safer.
She might be shocked at first. Sakura has always known Naruto as someone who is very attached to Konoha. If his leaving is because of her, she could feel guilty. She might try to stop him, asking him why he's doing this and telling him that he doesn't have to go.
They could leave because of a prophecy. Some ancient prophecy might state that they need to leave Konoha to fulfill a greater destiny elsewhere. So they trust in this prophecy and leave their home.