Hie thee North, Jon Snow.

Do what Rhaegar and Lyanna couldn't quite manage; what Ned Stark should have done but couldn't bring himself to: win the war if you must, but then pack up your shit and head North. Not to Winterfell, leave that to Sansa and Arya to figure out. Go wildling. Join up with the Free Folk as just another sword, a nobody from nowhere.

Don't leave a forwarding address. Don't wait around to celebrate the dead or the living. Get on the first horse you can find and leave the squabbling to those who revel in it.

You have Aemon's example. You have Mance Rayder's example. You've been told repeatedly that you're no Stark, beginning with Catelyn. Even Ned was getting ready to tell you that you're something else besides. Take it, live it, and leave all the rest behind.

Just my opinion, based only on what the books tell me. I have no expectation that either George or the showrunners will follow up on the trail of crumbs that seems to be there for Jon.