Fic where Jon rides south with Robb.
I just thought of the perfect story to write where Jon doesn't go to the wall, but instead, leaves to go some other place in the North. Like Last Hearth, Bear Island, or White Harbor. But when the news of Ned's arrest spreads through the realm and Robb calls the banners, he travels back to Winterfell and marches south with Robb.
When they cross over the Neck and meet up with Cat, she and Jon will probably avoid each other, but the betrothal at the Twins happens all the same. Eventually, the battle of the Whispering Wood happens all the same, but with Jon and Ghost fighting right alongside Robb and Greywind. Jaime is captured all the same, they get the news that Ned was killed and Robb is still crowned KITN.
As the war goes on, Jon becomes Robb's right-hand man and receives some glory for himself. When Robb announces his intention to send Theon away to treat with his father, Jon tries to convince him not to, but Rob has made up his mind and sends Theon away.
Robb gives Jon the task of watching Jaime since he absolutely trusts him, so Cat won't get to release him in this AU. But when they receive word that Theon has captured Winterfell, Robb sends him back up North to retake the castle and capture Theon, (this way, he isn't around for the Red Wedding.) But by the time he gets there, it's already too late. Bran and Rickon are presumed dead and the castle is sacked. But deep down, he still has hope that his brother might still be alive out there somewhere, so he and his soldiers start to search for any survivors and begin preparing Winterfell. And also start chasing the Ironbornn out of the North.
Back down south, Robb, who has just married Jeyne Westerling receives word from Jon about what happened. And after hearing that Sansa was married to the Imp, he decides to legitimize Jon and make him his hero. Cat is totally against this and even goes as far as to accuse Jon of killing the boys. This of course angers Robb to the point where he shouts at her and declares that until he has a son, Jon is the heir to Winterfell. Except this time, it's made publically known.
Things still go the way they do in canon. Robb still dies at the Twins, and Roose is still declared Warden of the North and marches up North to solidify his new status. However, with Jon up there, and having been legitimized as Jon Stark, things are more complicated for him now. This will become a full-on Northern civil war.
So, between dealing with the Ironborn invading the North, dealing with the traitorous Boltons, and reports of a wilding army marching on the wall, Jon is gonna have his hands pretty full. I can see this being labeled, The War for the North.