There are so many possibilities. He could explore a hidden cave in the forest where there are strange markings on the walls. These markings could be a map to a powerful ninja weapon. Naruto might also have to deal with a forest spirit that is angry because humans have been polluting the forest. So, he has to find a way to make peace with the spirit while living in the forest.
In the fanfiction, Naruto could have adventures like finding a secret waterfall in the forest that has special chakra - enhancing properties. He might have to fight off bandits who are trying to take over the forest for their own evil purposes. And he could also meet a hermit who teaches him some new jutsu that are specific to the forest environment.