Well, he could expect adventures that test his limits. Maybe in this different dimension, there are no villages and ninjas are more like lone wolves. Naruto would have to learn to survive in this new environment where the rules are different. He might also find that his reputation as a hero in his own world means nothing here, and he has to prove himself all over again. This could lead to him having to fight for respect and to make new friends. And of course, there could be new and strange creatures that he has to either fight or befriend.
Naruto can expect adventures that change his perspective. In a different dimension, the values and beliefs might be very different. He could meet people who see the world in a completely opposite way to him. For instance, in his world, he values friendship and teamwork highly, but in this new dimension, individual strength might be more important. This would make him question his own beliefs and maybe even learn from the new ones. He might also discover new forms of power within himself as he faces the challenges of this strange new dimension.
Another possibility is that he gets involved in the early days of the Akatsuki. He might try to change the course of the organization, perhaps by convincing some of its members to abandon their more evil plans. Since he's already a retired and experienced ninja, he has a different perspective on things compared to when he was younger.
In this kind of fanfiction, Harry might encounter new magical creatures that don't exist in his own dimension. For example, he could meet some kind of shape - shifting beasts that can change into any form they like.
Perhaps he'd meet a different Hokage. One who has led the village in a completely different way than in his own dimension. Naruto could learn a great deal from this Hokage about leadership and different ways to protect the village.
Naruto might have an adventure where he teams up with local ninjas in Whirlpool to fight against a common enemy. This enemy could be someone or something that is threatening the peace of the region. And during this adventure, Naruto can learn new combat techniques from his new allies.
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.
He could go on a road trip across America. Imagine Naruto seeing the Grand Canyon or the Statue of Liberty for the first time. It would be an amazing sight for him.
In the alternate dimension, Naruto could find that the Akatsuki are actually the protectors of the villages. This would completely change his view of the world. He would have to re - evaluate his ideas about good and evil and decide whether to help them or oppose them depending on their true motives.
When Naruto goes to a parallel dimension in fanfiction, it's a whole new world of possibilities. He could encounter a dimension where his parents are still alive. This would be a huge emotional moment for him. He might also find that the Akatsuki in this dimension has different motives or is even a force for good. Naruto's own values and beliefs would be put to the test as he tries to understand and navigate this strange new place. His usual techniques like the Rasengan might not work as effectively, forcing him to learn and innovate on the fly.
Naruto's positive and determined personality will drive him to keep exploring the new dimension. His never - give - up attitude means he won't be easily discouraged by the initial difficulties. For example, if he encounters a powerful foe, he'll keep trying to find a way to defeat it rather than running away.
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.