Jon Snow is now the King of the North and he really only has one objective: prepare for the White Walkers. Though Jon definitely has other things he needs to worry about, all he cares about is making sure his people are ready for the army of the dead that is currently heading south. While Jon prepares to train everyone that's able to fight, Sam has discovered there's a plethora of dragonglass at Dragonstone that could turn the tide in the war against the dead. So will Jon visit Dragonstone on Game of Thrones? It seems likely.
After grabbing a book from the restricted section of the Citadel library, Sam discovered there's an underground mountain of dragonglass at the Dragonstone castle. And since it's been confirmed on the show that dragonglass is one of the few things that kills White Walkers, he quickly sent a letter to his bestie Jon, to let him know. The only issue is Daenerys just arrived home at Dragonstone and she probably won't just let Jon drop by and grab some dragonglass. No, she'll want something in return. Most likely, she'll want a guarantee that when the inevitable war between herself and Cersei comes, he'll be on Team Daenerys.
However, based on the preview for the second episode, it's clear the Northerners won't be too thrilled with the idea of working with a Targaryen. Little do they know, Jon is half Targaryen himself, which will probably come up at some point this season. The point is, even though Jon is King, he'll probably ruffle some feathers if he decides to work with Daenerys to get some dragonglass. Not that that'll stop him.
Jon will do whatever is necessary to make sure his people are prepared for the long winter and if that means working with Daenerys, there's no doubt he'll do it. Therefore, it looks like Jon is about to take a trip south. However, there is always the alternative option of just sending someone else to make contact with the Mother of Dragons in his stead, before he travels all the way there himself.
Still, knowing Jon, he'll want to make the journey himself. Plus, it'll be a better show of faith if the King of the North himself goes to meet Dany rather than just sending someone else. And, more importantly, it's time these two Targaryens finally met face-to-face. It's been a long time coming and it'd be shocking if the show didn't take this perfect opportunity to finally connect the two.
In other words, Jon better pack his bags. It looks like he has a long journey ahead of him.