After some scenes in the North, our favorite King in the North will make his way to Dragonstone sometime early in the season to meet with the Dragon Queen—his aunt Daenerys. He will be greeted on the shores of Dragonstone by Missandei, Tyrion, and some Dothraki, and will exchange a formal handshake with the Hand of the Queen. Jon and Queen Daenerys will later have a scene walking together along the battlements of Dragonstone. When the Ironborn arrive on Dragonstone, there will be a tense meeting between Jon and Theon Greyjoy—one in which Jon grabs Theon roughly by the lapels and shakes him, before stalking off in a huff.
At some point after arriving on Dragonstone, Jon will also have a scene with Daenerys on a beach near some oceanfront caves, where they talk, and he meets and pets at least one of her dragons. Judging by the color of the reference head used, the dragon will be Rhaegal—who is named for Jon's father, Rhaegar Targaryen. Excuse me while I puke from the excitement!
Jon will also be present in a scene set at the Dragonpit in King's Landing, in which he and Daenerys—under a temporary flag of truce—display a wight to Cersei as proof of the White Walker threat. This scene—we'll just call it the Dragonpit scene—could possibly involve up to 17 of the major cast members, including Jon, Cersei, Jaime, the Mountain, Qyburn, Bronn, Euron, Daenerys, Tyrion, Jorah, Missandei, Varys, Theon, Davos, Brienne, Podrick, and the Hound.
Updated 12/16/16: Kit Harington has been spotted filming in furs at the Wolf Hill Quarry location, which is obviously set in the North. The location looks like an iced-over lake, with some sort of island or rock in the middle. Also spotted at Wolf Hill: Iain Glen (Jorah), Rory McCann (Sandor Clegane), and Kristofer Hivju (Tormund Giantsbane). Additionally, 300 extras dressed as wights have been used for the shoot. All of this backs up leaked info from /r/freefolk, as well as other set leaks, that Jon will capture a wight to bring to King's Landing. Director Alan Taylor was also present at the quarry, which essentially confirms that the events taking place there will happen in episode six.
Updated 1/16/17: Kit Harington has been spotted in social media photos hanging out around Iceland, which appears like it'll be used for outdoor scenes representing the journey north of the Wall. This wight-capturing leak is beginning to look more and more like the real deal.
Updated 4/24/17: While primary filming was still taking place, Kit Harington was spotted at the quarry set (among others) in Iceland, along with the actors for Jorah, The Hound, Davos, Gendry, Beric, and Tormund. That's a big ol collection of some of our favorite characters, all ready to take on this crazy wight expedition. As far as what Jon will be up to this season, Harington claimed in an interview with Huffington Post that "I certainly did more this season than I've ever done. I think every actor on it did more action, had more action, had more scenes." It also looks like we're going to get some Ghost action this season; the white wolf who plays Ghost was doing some filming recently along with another mysterious gray-and-brown wolf.
What appears to be a legitimate piece of leaked concept art depicts a scene supposedly from the season seven finale: Tyrion, Bronn, Jon Snow and a Lannister soldier all stand in front of what can only be the entrance to the Dragonpit. Harington also let slip in another interview with Moviefone that he's "eagerly" awaiting the script for season eight, and that "next season, [Jon Snow] might go through a big change." This is exciting news, because it pretty much verifies that Jon Snow will survive this season, unless Harington is lying in his interviews (as he has been known to do). Finally, the promo stills show us Jon staring sorrowfully up at something in what looks like the crypts of Winterfell. Because of the Boltons' depredations, Ned probably doesn't have a statue yet there. Is it too much to hope that Jon is looking up at Lyanna's likeness in this scene? If so, that implies that he learns his true identity, and soon.