They could go on adventures in the forest outside the village. For example, they might encounter strange creatures that the cat's instincts help them avoid or deal with.
They might have an adventure where they have to save a group of kittens from a group of bandits. The cat would use its small size and agility to scout ahead, and Naruto would use his ninja skills to fight the bandits. This would be a really exciting adventure that shows the teamwork between them.
Perhaps they get involved in a mystery within the village. The cat might notice some strange behavior among the villagers that Naruto overlooks at first. Together, they start to investigate, and it leads them to uncover a plot against the Hokage. This adventure would be full of twists and turns as they try to stop the bad guys and protect the village.