In some fanfictions, if Jon Snow goes to Old Valyria, he may meet characters from the past. He could interact with ancient Valyrian families or even those who were involved in the events that led to the Doom. This could give him insights into the history of the world and how it has shaped the present, and potentially give him ideas on how to deal with the threats in Westeros.
Maybe to seek answers. The secrets of his parentage might be somehow linked to Old Valyria. He could believe that going there would give him a better understanding of who he really is and his place in the world.
The wildlings might be his allies. After all, Jon Snow has had interactions with them before. They are fierce fighters and could fight alongside him against a common enemy.
Well, it could be about Jon Snow leading his men into a great battle against the White Walkers. Maybe he discovers new strategies or forms unexpected alliances during the war.
One possible plot twist could be that Jon Snow goes back in time and accidentally changes something that leads to a completely different future for the Stark family. For example, he might prevent Ned Stark from going to King's Landing, which would change the power dynamics in Westeros entirely.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
His relationship with his father, Ned Stark, would be different. He could finally have a real father - son relationship instead of the hidden one. He might be able to learn from Ned and become an even better leader in the North.
In this fanfiction, one of the key battles Jon Snow might participate in could be the Battle of the Whispering Wood. His skills as a fighter would be put to good use there, sneaking around and taking out enemies. Another could be a fictional battle near the Wall, where he defends against some new threat that has emerged during Robb's war.
He might go back to Winterfell and claim his rightful place as a Stark. This would change the whole power dynamic in the North and also his relationship with his siblings.
A great deal of Jon Snow and Iron Throne fanfictions focus on his relationships. For example, his relationship with Daenerys could be very different in fanfictions. In some, they rule together on the Iron Throne, combining their claims and powers. In others, they are at odds, with their relationship being a major obstacle in Jon's path to the throne. And of course, there are fanfictions where his Stark family ties also influence his actions regarding the Iron Throne, as loyalty to his family is a strong part of his character.