His reign would likely be one of justice and fairness. Jon has always been a character who values honor and doing what's right for the people. He would probably focus on rebuilding the Seven Kingdoms after all the destruction from the wars. He'd try to unite the different regions, regardless of their past grudges.
Jon Snow's reign as king would be unique. He has a connection to both the North and the South. This could lead to a more unified Seven Kingdoms. He would use his leadership skills, which he developed through his many trials, to make decisions that are in the best interest of all. He would respect the traditions of each region while also bringing in new ideas. For instance, he could encourage trade between the different kingdoms, promoting economic growth.
Jon's reign as king could be a time of great change. Given his experiences with the Night's Watch and the Wildlings, he would have a more inclusive view. He might introduce policies that benefit the smallfolk more directly. For example, improving farming conditions and reducing the power of the corrupt lords. Also, he would surely strengthen the defenses of the realm against any future threats.