It could be a rogue ninja from another village who wants to capture Naruto and Ino for their own gain. Maybe he heard about Naruto's Nine - Tails power and Ino's family's special techniques and plans to sell them to the highest bidder.
Well, perhaps in a 'naruto and ino run away' fanfiction, they run away because they discover a dark conspiracy within the village that targets them. They run to find an ally in a far - off land. As they journey, they start to rely on each other more. Ino uses her mind - reading skills to avoid enemies, and Naruto uses his strength to protect them during battles.
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.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
Maybe they run away to avoid an arranged marriage. Sakura, being strong - willed, leads the group. Ino could use her mind - transfer jutsu to gather information on safe places to hide. Hinata is there for her gentle support, and Tenten provides her weapon - skills for protection. They end up in a hidden valley where they train in secret.
It could be a rogue ninja who has a vendetta against their village. This ninja might see the girls as easy targets or as a way to get back at the village. He could be tracking them down during their run - away journey.
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.
Perhaps Naruto discovers something about Itachi that the rest of the world doesn't know and he needs to run away to protect that secret. It could be a powerful jutsu or a message that could change the balance of power in the ninja world.
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.