I'd like to cover some of the upcoming stories and side stories we'll (probably) be getting come the future patches.
Raid: Pandaemonium
It seems the teaser implied that Pandemonium is a being, and not a location. It will be interesting to see of Lahabrea is our main associate for the story. Hopefully it fleshes him out more.
Alliance Raid: Myths of the Realm
Emet-Selch teased it when he mentioned that we didn't even know who they really are. Seeing as he was on the Convocation, I think the implication is that the Twelve aren't just the Convocation misremembered through the ages, otherwise why would he tease it as a mystery?
Trials: No spoilers here, but it's looking like 6.1 will have the EX version of the final boss, so the side story trial should start on 6.2. However, seeing as they're changing how the MSQ is normally done, I wonder if they'll move an epic "story trial" fight to 6.5 or not, or even make the side content all of the future trials. Personally, I'm hoping for the Elemental Archfiends from FF4, but that does bring to question as to what they may be.
Relic weapons: Chances are we'll have another set of instanced zones, so it'll be interesting to see where we're going this time.
Beast tribes: We know two tribes (Loporrits and Matanga), but the third is anyone's guess. I'm betting the Matanga quests will feature the more aggressive tribe we see in the Azim Steppe.
Crafter/gatherer endgame: No clue, but I wonder if this will crossover with the traditional city rebuild content again, and if they're going to do a new version of the Ishgard Restoration or go somewhere new.
Island Sanctuary: Probably won't have a whole lot of story to it, but it will still be interesting to see.
MSQ: Obviously, we've known the MSQ will be going in a new direction.
I'm curious to see if it becomes more anthology like, with us exploring some of the mysteries Emet-Selch teased us with.