Their relationship could start as comrades on a mission. As they leave Konoha together, they'll have to rely on each other. Naruto's sunny personality might gradually break through Samui's more reserved nature. They could start sharing their pasts, with Naruto talking about his lonely childhood in Konoha and Samui sharing about her life in the Cloud Village. This sharing would bring them closer, and they might develop a deep friendship at first, which could potentially turn into something more romantic as they face more and more challenges together.
One possible plot could be that Naruto and Samui are on a mission outside Konoha when they receive some crucial information that puts Konoha in danger. However, they realize that there are traitors within the village who would stop them from using this information to save it. So, they decide to leave Konoha temporarily to gather more evidence and allies. Along their journey, they face various challenges and also start to understand each other better, with Naruto's determination rubbing off on Samui and Samui's calm and strategic thinking helping Naruto in different situations.
Maybe there are some dark secrets within Konoha that he discovers in the fanfic. These secrets could be related to the treatment of certain individuals or something more sinister about the village's leadership. Discovering such things could make Naruto decide to leave in order to distance himself from the corruption or unfairness.
Sakura would probably be very worried. She has always cared about Naruto deep down, so she might be constantly trying to find a way to bring him back. Kakashi, on the other hand, would likely understand Naruto's reasons to some extent. He might be sad but also respect Naruto's decision. As for Sasuke, if he is in the village at the time, he could be conflicted. He and Naruto have a complex relationship, and Naruto's leaving might make him realize how much Naruto actually means to him.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.
In a 'naruto and kushina leaves konoha fanfic', perhaps they leave due to a threat to Naruto's safety that the village can't fully protect against. Maybe some secret organization is after him and they feel they have no choice but to go into hiding outside Konoha.
In a 'Naruto Namikaze leaves Konoha' fanfic, it could be that Naruto is framed for a crime he didn't commit. The villagers turn against him, and even his friends start to doubt him. Feeling betrayed and alone, he decides to leave Konoha. As he travels, he meets other outcasts who have also been wrongly accused, and together they form a group to clear their names and seek justice.
One idea could be that as Naruto leaves Konoha, he encounters a powerful and ancient creature in the wild. In a battle with it, the extreme stress and need to survive unlocks his hidden bloodline. This new power could be related to some kind of elemental control that is unique to his clan, like a special form of wind manipulation that is far more powerful than what he had before.
One possible plot could be that Naruto leaves Konoha due to some misunderstanding. Maybe he feels unappreciated in his relationship with Sakura (Narusaku). He might go on a journey to find himself. Along the way, he could encounter new enemies and also make new friends who help him see things from a different perspective.
In this kind of fanfic, one possible scenario could be that Naruto leaves Konoha due to feeling misunderstood. Maybe he has been wrongly accused of something and decides that he can't stay in a place where people don't trust him.