A really interesting plot would be if Luke's time travel was accidental and he ended up in a parallel universe. In this universe, the roles of the Sith and the Jedi are reversed. He would have to figure out how to get back to his own universe while also dealing with the strange new world he's in. Here, he might learn things about the Force that he never knew before, like different ways to use it that are unique to this parallel universe.
Another interesting plot is Luke traveling to the future. He discovers a galaxy in chaos due to a new, powerful dark force. He has to adapt to new technologies and new forms of the Force while also finding a way to defeat this new threat. He might meet descendants of his friends and foes, which would add an interesting dynamic.
One idea could be Luke traveling back in time to the Clone Wars era. He could meet his father, Anakin Skywalker, before his fall to the Dark Side and try to prevent it. Maybe he uses his Jedi skills to influence Anakin in a positive way, like teaching him some advanced Jedi techniques that could strengthen his connection to the Light Side.
One idea could be Luke traveling back in time to the Clone Wars era. He could meet Anakin Skywalker before his fall to the Dark Side and try to change his fate. Maybe he'd use his knowledge of the future to prevent certain battles or alliances that led to the downfall of the Jedi Order.
One plot idea could be that Luke Skywalker discovers an ancient Jedi artifact that has a connection to Revan. As he delves into its secrets, he starts having visions of Female Revan. They then start communicating across time and space, sharing their knowledge of the Force and different eras of the Jedi. This could lead to Luke learning new ways to combat the dark side from Revan.
One idea could be Luke struggling to hide his true identity while at the Imperial Academy. He might have to pretend to be a loyal Imperial while secretly trying to undermine their operations. For example, he could subtly sabotage training exercises or misdirect fellow cadets.
One plot idea could be Luke struggling to balance the dark and light sides within him due to his new position as heir to the Empire. He might face internal conflicts as he tries to reform the Empire from within. Another could be him having to deal with former Rebel allies who now see him as a traitor. And perhaps he discovers a hidden power within the Empire that could either save or destroy the galaxy.
One idea could be Anakin traveling back in time to prevent his fall to the dark side. He could use his knowledge of the future to avoid the events that led him astray, like not trusting Palpatine. Another plot could involve him traveling to a time after his death and seeing the impact of his actions on the galaxy, which could be a moment of redemption for him. And perhaps he travels to a completely different era in the Star Wars universe and has to adapt to new cultures and powers while also dealing with his own inner turmoil.
One idea could be that baby Luke Skywalker time - travels to the era of the Old Republic. He could end up being found by a Jedi Master there and starts his training much earlier. This would completely change the course of the Star Wars timeline as he'd be much more powerful by the time the original trilogy events are supposed to occur.
Some fanfics might have Anakin time travel to a time when the Jedi Order was first founded. He could learn from the ancient Jedi teachings and bring that knowledge back to his own time to reform the Order. Or he could travel to a post - Galactic Empire era, seeing a galaxy that has either recovered or is still in chaos from his actions as Vader, which would be a huge motivation for him to go back and change things.
One idea could be that she discovers her father's legacy in a hidden Jedi temple. Another could be her having to face an ancient Sith threat that was once defeated by Luke. Maybe she teams up with new characters to protect the galaxy like her father did.