Often, Naruto is sent back to a time when he can prevent a tragic outcome or gain crucial knowledge. It could be to the time before his village was attacked or when a key character made a fateful decision.
Madara Uchiha could also be a main antagonist. If Naruto goes back to a time when Madara was still alive and plotting, Madara would surely oppose Naruto's attempts to change the future. He has his own grand plans for the world and wouldn't let Naruto interfere easily.
One idea could be Naruto going back to the time when the Uchiha clan was still intact. He could try to prevent the massacre by changing certain events or by influencing key people. Another plot could be him traveling back to his own childhood and using his future knowledge to become an even more powerful ninja earlier, like learning advanced jutsus much sooner.
Well, one thing that could happen is that Naruto, with his knowledge of future events, could easily ace the written part of the Chunin Exams. He might also be able to prevent some of the chaos that Orochimaru caused during the exams. For example, he could warn the proctors about Orochimaru's infiltration in advance.
Naruto's power of the Nine - Tails would be a major factor. In the past, the Nine - Tails was feared and hunted. If Naruto shows up with the power under control, it could change how people view the beast. His chakra reserves, which are huge because of the Nine - Tails, could allow him to perform feats that were previously thought impossible in the past, like quickly rebuilding a village or fending off a large - scale invasion on his own.
Well, when it comes to Naruto time travel and Rinnegan in fanfics, it's often about exploring new storylines. Maybe Naruto himself gets the Rinnegan and travels back in time to train his younger self. This would make him a much more powerful ninja at an earlier stage and could completely change the power balance in the Hidden Leaf Village and among the other ninja villages as well.
One possible plot twist could be Naruto changing the past in a way that completely alters the future relationships. For example, if he prevents a certain event that led to a character's death, it could change the whole dynamic among the characters. Another twist could be that Naruto discovers that the past is not as simple as he thought, and there are hidden forces at work that he didn't know about in his original timeline.
Another reason might be to stop a greater threat. Maybe there was a hidden enemy in the past that they didn't know about before, and by traveling back, they can stop this enemy from becoming too powerful. In some fanfictions, they discover that a small event in the past was the root cause of a much larger and more dangerous future situation.
One common theme is redemption. Naruto often goes back in time to right the wrongs of the past, whether it's saving a fallen comrade or preventing a great disaster. Another theme is self - improvement. He uses the knowledge from his future self to become a better shinobi faster.