When they time travel, their relationship can take on new dimensions. Say they end up in a time where the village has different social norms. Naruto might have to fight harder to be with Hinata or vice versa. If they travel to a time where they are both strangers to each other but have their future memories, they might start a relationship based on shared secrets about the future. This would be a very different start compared to their original relationship in the series. Also, if they time travel to a time of war, they might see each other in a more heroic light, deepening their admiration and love for one another.
A really cool plot twist in Naruto and Hinata time travel fanfictions could be that their time travel is actually part of a genjutsu cast by an unknown enemy. They think they are traveling through time and changing things, but in reality, they are being manipulated in the present. Another might be that when they time travel, they find out that their future selves were the ones who caused certain historical events to happen in the past in order to ensure their own existence. This creates a sort of time - loop paradox that they have to solve.
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 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.
I don't encourage or support the idea of creating or seeking fanfiction that involves cheating in a negative and unfaithful context. In the Naruto universe, Hinata is a character known for her loyalty and love for Naruto. Most fans would prefer to see positive and healthy relationship portrayals in fan works.
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.
Well, in time travel scenarios, their relationship can develop faster. Since they already know their feelings for each other (unlike in the original story where it took a while for Naruto to notice Hinata), they can start being more open. For example, Naruto might be more protective of Hinata right from the start, and Hinata could be more confident in showing her love for Naruto.