Naruto's character can develop in several ways. Away from Konoha, he is forced to rely more on his own instincts and less on the support system he had in the village. He might become more self - reliant and learn to make decisions without the immediate guidance of his friends or mentors like Kakashi. For example, when facing a new type of enemy, he has to quickly figure out a strategy on his own. This makes him grow in confidence and his ninja skills improve as he has to adapt to different fighting styles and terrains.
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.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he has reached a level in his training where he believes he needs new experiences and challenges that Jiraiya can no longer provide.
Some fanfictions might feature rogue ninja as antagonists. These rogue ninja are after the bounty on Naruto's head or they are trying to steal Jiraiya's knowledge. They attack Naruto and Jiraiya during their travels, making it difficult for them to reach their destination.
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.
Maybe they leave to find a better way to protect Konoha. They might think that by exploring the outside world, they can gain new knowledge and powers that will be useful for their village in the long run.
It would be a huge blow to Konoha. Naruto is a hero in the village, and his departure would leave a big leadership void. The villagers would also lose a great source of inspiration. Hinata is from a respected clan, and her leaving would also have an impact on the clan's standing in the village. Morale among the ninjas might drop as they see two important figures leave.
Well, it would be a big loss for Konoha. Naruto is a powerful ninja, and his absence would mean one less strong fighter to defend the village. Ino, too, has her unique skills in mind - related jutsu and communication. Their departure might also lower the morale of other ninja, especially those who were friends with them or looked up to them.
Maybe they leave to find a cure for a strange disease that has started to affect the ninja world. Jiraiya has some clues about a special herb in a far - off region and they embark on a journey. During this, Naruto learns about the importance of perseverance from Jiraiya. They face many enemies who don't want them to succeed in their mission.
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.