Shikamaru might be sent to find Naruto. He's known for his intelligence and strategic thinking. The village elders might trust him to be able to track Naruto down and either convince him to come back or at least find out his intentions. Shikamaru also has a certain respect for Naruto and would understand his motives to some extent.
It could be that some of the village elders or leaders send someone to go after her. They might see her running away as a threat to the village's stability or as a potential loss of a valuable asset. Maybe they send a team of ANBU to track her down and bring her back, whether by force or persuasion.
Sakura might try to stop Naruto. She is one of his closest friends. She cares about him deeply and would be worried about his safety. Also, she would understand that running away is not the best solution to whatever problems he is facing.
Kakashi could be another one. As Naruto's former sensei, he knows Naruto's capabilities and potential. He would try to stop Naruto from running away because he believes that Naruto has a future in Konoha and running away isn't the solution to whatever problems Naruto is facing.
Another reason could be for the sake of protecting the village. Maybe he discovers some sort of threat that he believes he can only face by leaving Konoha. He doesn't want the village to be in danger because of him, so he runs away to draw the danger away from Konoha.
Perhaps he would journey to the Hidden Cloud Village. There he could meet new people and learn different techniques. He might also try to bridge the gap between Konoha and the Cloud Village, starting from outside Konoha's boundaries. This would be a way for him to still work towards peace on a larger scale, but away from the restrictions he felt in Konoha.
One possible reason could be feeling ostracized. In the Naruto world, being different is often not easily accepted. As a female Naruto, she might face even more scrutiny and prejudice. Maybe she's tired of the constant expectations and the way she's treated in Konoha, so she decides to run away to find a place where she can be herself.
He could run to the Land of Waves. He has a connection there from his early mission. The people there were friendly to him, and he might find some peace and acceptance among them. It's a place where he could start anew, away from the chaos of Konoha.
Perhaps Goku. Goku has a big heart and he's always ready to help those in trouble. He could sense Bulma's distress and come to her aid.
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.