They might run away to avoid a conflict that their villages are about to be dragged into. Naruto and Sasuke, being the powerful ninjas they are, don't want to be used as tools in a war, so they decide to run away.
One possible plot could be that Naruto and Sasuke run away to find a place where they can train without the interference of the Hidden Villages. They might be on a quest to become stronger together, away from the prying eyes of their respective villages which have different expectations of them.
Maybe he's running away from the pressure in the village. There are always high expectations on him, and he might feel suffocated and need some time alone to figure things out.
One consequence could be that his friends worry about him a great deal. They might go on a search for him, which could put them in danger as well. After all, they care about Naruto deeply and won't just let him disappear without trying to find him.
He could meet some of Iwa's powerful ninjas. Maybe Onoki, who could either see him as a threat or an opportunity. There might also be some young Iwa ninjas who are curious about Naruto and his abilities.
He might meet some of his distant Uzumaki relatives. There could be elders or other Uzumaki clan members who have valuable knowledge about his family and their special abilities.
Perhaps he is running away from danger in Konoha. There could be a threat that he believes he can't face directly in the village, and he thinks Whirlpool might offer some sort of sanctuary or a way to become stronger in relative safety.
Maybe he's running away from some kind of danger or threat in his home village. There could be a group or an individual after him, and he believes that Kumo would be a safer place. It could also be related to some political unrest in Konoha that makes him feel like he has to leave, and Kumo seems like a viable option.
Maybe he feels misunderstood by his family. In many Naruto stories, his family situation can be complex. If he's 'godlike', he might have powers that his family doesn't understand or fears, leading him to run away to avoid conflict or being treated differently.
In this fanfiction, Naruto might run away to Iwa because he feels misunderstood in Konoha. Maybe he discovers some secrets related to his family that make him think Iwa has the answers. He could face many challenges on his way there, like avoiding capture by Konoha ninjas who think he's a traitor.