In many such fanfictions, Naruto and Hinata might be sent back in time through some magical or jutsu - related means. Once they meet their parents, it could be a very emotional moment. Naruto might see his father Minato and mother Kushina, and Hinata could meet her father Hiashi. They could learn a lot about their families' pasts and perhaps even change some things for the better in the timeline.
They could witness historical events. For example, Naruto might see Minato become Hokage. Hinata could see how her family's status was in the past. It would be interesting to see how they interact with their parents. Naruto might be eager to show off his skills to his father, while Hinata would probably be more reserved in front of her family.
Well, there's a fanfiction where Naruto travels back and meets Itachi as a young Uchiha. Naruto tries to understand Itachi's motives better and in the process, he gets involved in the internal Uchiha affairs. It's a great read as it shows a different side of Itachi and how Naruto's presence could have changed things. Also, 'Naruto's Time - Jump to the Uchiha Era' is a fanfic that focuses on Naruto learning about the Uchiha's unique abilities and culture during his time - travel adventure.
The parents' relationship could also set an example for Naruto and Hinata. If Kushina and Hinata's mother had a strong, loving relationship, Hinata might be more inspired to be as loving and supportive in her relationship with Naruto. Similarly, Naruto could learn from his father's respect for Hinata's family and carry that forward in his relationship with Hinata.
One common theme is redemption. Hinata might go back in time to right the wrongs she or others have committed in the original timeline. Another theme is love. Since Hinata has feelings for Naruto, time travel can be a way to explore a different kind of relationship development, like falling in love all over again in a different context.
Another possibility is that Naruto travels to a time when the Uzumaki clan was facing a great threat. He could use his skills and knowledge from the future to help them. Maybe he teams up with young versions of his parents or other Uzumaki members to fight off the enemy. This could lead to a whole new understanding of his heritage and his own powers.
One possible plot could be that Naruto and Hinata travel back in time to their childhood days. They could use their knowledge of the future to prevent some of the tragedies that happened. For example, Naruto might try to stop the Nine - Tails attack on the village in a different way, and Hinata could help by using her Byakugan skills more effectively from an earlier age. They would also have the chance to change their own relationship dynamics. Maybe Hinata could be more confident around Naruto earlier, and Naruto could realize his feelings for her sooner.
A common theme is self - discovery. The daughter, when traveling back in time, often discovers new things about her family's past and in turn, about herself. For instance, she might learn about her parents' early struggles and how they overcame them, which gives her newfound strength and understanding.
One popular plotline is that Naruto and Hinata travel back to the time when the Uchiha clan was still intact. They try to prevent the massacre from happening, which changes the whole future of the ninja world. Another plotline could be them going back to their childhood days. Hinata gets a chance to be more confident around Naruto earlier, and Naruto realizes Hinata's feelings sooner, leading to a different relationship development.
Their relationship would likely become stronger. If they travel back in time, they already have the memories of their relationship in the future. So, Hinata might be more bold in expressing her feelings, and Naruto would be more aware of her importance to him from the start.