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.
One interesting plot could be Naruto and Hinata traveling back to the time when the Uchiha clan was still intact. They could try to prevent the massacre. Maybe Naruto, with his future knowledge and Hinata's byakugan skills, would work together to change the fate of the Uchiha, which would have a huge impact on the future of the ninja world.
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.
One great one I found has Naruto and Hinata's mom team up to change certain events in the past. It's really interesting to see how their different perspectives and knowledge of the future play out.
Well, it could be about them traveling back to prevent a great disaster that was supposed to happen in the future. Maybe something related to the destruction of the Hidden Leaf.
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.
It could be a time - traveling rogue ninja from the future who wants to change the past to gain power. This ninja might try to stop Hinata's mom from achieving her goals in the past.
Danzo could be a potential antagonist. Even in the past, he might be plotting against the Uchiha clan. If Sasuke and Hinata try to change things related to the Uchiha, Danzo could see them as a threat and try to stop them.
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.