Perhaps in a fanfiction, Jon Snow gets a castle that has a hidden magic. This magic could be the key to uniting the Seven Kingdoms in a more peaceful way than through war. He discovers ancient secrets within the castle walls that help him in his quest for a better realm.
Jon Snow could use the castle as a base to improve relations with the other kingdoms. He might hold diplomatic meetings there, inviting lords and ladies from all over Westeros. This would be a big change from his more battle - focused past.
If Jon Snow gets a dragon in fanfiction, he might face new challenges. People would be both in awe and envious of his newfound power. There could be plots against him not just from political rivals in Westeros but also from those who fear the power of dragons. He would have to learn how to control the dragon quickly. Given his noble nature, he might try to use the dragon's power for good, like protecting the smallfolk and rebuilding the war - torn regions.
One implication could be a shift in power dynamics. If Jon Snow has Blackfyre, he becomes a more formidable force, which might make other characters either fear or seek to ally with him.
In this fanfiction, the relationship between Jon Snow and other characters would be different. For instance, Sansa might view him as an even greater asset to the North. Theon would likely be in awe of him. His relationship with Arya could also be affected as they might plan new adventures together with the help of the dragon. And his enemies, like Cersei, would be more desperate to get rid of him as his dragon - powered presence would be a huge threat to her rule.
Daenerys Targaryen is a very likely candidate. Their connection through their Targaryen blood (Jon's true heritage) could be a strong basis for a marriage. They could join their forces, both having a claim to the Iron Throne, and rule Westeros together. Their marriage would also symbolize the unification of the North and the South, as well as the different Targaryen branches.
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.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.