Perhaps in this different dimension, female Naruto is a princess. But she still has her ninja spirit. She uses her skills in a different way, like using her agility to outwit court conspirators. And she might even start training the palace guards in her ninja ways secretly.
A possible plot is that female Naruto enters a dimension full of mythical creatures. She has to befriend some of them to learn about this new world and find a way to return to her own. For example, befriending a dragon that can help her fly over the strange terrains.
In fanfiction, if Naruto is sent to a different dimension, he might face all kinds of strange new powers and enemies. For example, he could encounter magic that is completely different from chakra. He would have to quickly adapt to survive. Maybe he'd find allies who are also lost in this new dimension and together they'd try to find a way back home while also dealing with the local threats.
Naruto might start by observing. He would watch how things work in the new dimension. For example, if there are new forms of energy, he'd study how people use it. Then he'd try to apply his ninja skills in new ways. Like if there are flying creatures, he could use his shadow clone jutsu to distract them while he figures out a way to either befriend or defeat them.
One idea could be Naruto being transported to a dimension where chakra doesn't exist, but he discovers a new form of energy and has to learn to use it from scratch. This would force him to adapt his fighting style completely.
A really exciting plot could involve Naruto getting trapped in a time - loop within the Juubi dimension. Every time he tries to find a way out, he ends up back at the starting point. He has to figure out how to break the loop by solving a mystery related to the Juubi's power. This would require him to interact with different versions of characters he knows, who may have different personalities and motives in this strange dimension.
One idea could be Naruto traveling to a dimension where all the villains have become heroes. He has to adapt to this new world order and figure out how to get back to his own dimension.
One interesting plot could be Naruto traveling to a dimension where the Akatsuki are the heroes. It would be a complete role - reversal, and Naruto would have to figure out how to interact with them. Another could be a dimension where everyone has a different type of chakra, like water - based chakra for all shinobi, and Naruto has to adapt his skills.
He might face different types of chakra and powers that he's not used to. In a new dimension, the laws of nature regarding ninjutsu could be completely different. For example, his Shadow Clone Jutsu might not work as effectively if the chakra in that dimension behaves in an unexpected way. Also, he could encounter new and strange creatures that have abilities he has never seen before, making it difficult for him to fight or even communicate with them.
One idea could be that Naruto travels to a dimension where all the female characters from different Naruto arcs are united. They all fall for his unique charm and his skills as a ninja. He has to balance his new relationships while also finding a way back to his own dimension.
One idea could be Naruto arriving in a dimension where chakra doesn't exist and he has to learn new powers. Another could be him meeting alternate versions of his friends in different dimensions, like a super - evil Sasuke in one dimension. Maybe he also discovers a dimension where the Akatsuki are the good guys and he has to figure out how to work with them.