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.
One possible reason could be the constant scrutiny and pressure he faces in Konoha. Everyone has high expectations of him as the Jinchuriki of the Nine - Tails. He might feel suffocated by all the attention and the responsibility thrust upon him. Another reason could be the lack of true understanding from some of the villagers. Despite his efforts to protect Konoha, there are still those who look at him with distrust because of the Nine - Tails inside him.
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.
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.
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.
Maybe in the fanfic, Naruto has faced too many political intrigues within Konoha. He has always been loyal to the village, but if he constantly encounters backstabbing or unfair treatment from some of the village's leadership or clans, it could lead to his weariness.
She could encounter other outcasts. There are likely other ninjas or people in the world who have left their villages for various reasons. By meeting them, she could form a new group, a sort of 'family' of misfits. They could travel together, sharing their skills and stories, and maybe even start a small community away from the traditional ninja villages.
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.
One reason could be that he feels misunderstood by the villagers. Despite all he has done for Konoha, some still hold grudges or are afraid of his power. Another might be that he wants to explore the world on his own terms, away from the responsibilities and restrictions of Konoha. Maybe he also feels a sense of loneliness there, as he has lost many important people and the village constantly reminds him of those losses.