The title of this post is simply "Hardhome" because it's now a word and an episode that will be the reference point for television as spectacle and payoff and worldbuilding.
And while Hardhome will be known for that part that's set at, well, Hardhome, the rest of the episode needs to get the credit it deserves.
After Hardhome, the payoff of Tyrion and Dany meeting is one we've all wanted for a long time. And somehow, without a single dragon scale, these scenes of the new Targaryen alliance give us everything we wanted. Tyrion reasons through all the different scenarios, and whether or not to keep his own head/exile Jorah being a case study and a sort of test for him to show Dany his worth.
One of the most memorable lines this season is from Dany - "I"m a queen, not a politician." It's not so much a statement of fact and the relationship between monarchs and the smallfolk as it is a naive statement by Dany showing the realpolitik she lacks, and Tyrion can provide.
If Tyrion worked in Washington, DC, he would be known as "former White House chief of staff" and for good measure, "former Treasury secretary." He would be much sought after. He could start his own firm, he would be paid millions of dollars for his advice. In Westeros, his dad tried to kill him.
Anyways, being former Hand to the King is an asset that Dany sorely lacks, as she operates on the assumption the smallfolk will rise in support of her. The War of Five Kings can work two ways. It can weaken the lords from being so battle worn that they are vulnerable (except the Valemen and the Dornishmen). But on the other side, the smallfolk are warworn as well, tired of the fighting...as Jorah said in season one
the common people pray for rain, healthy children and a summer that never ends. It is no matter to them the high lords play their game of thrones.
so they may have a "call me when you're done" sort of attitude. They've already, in their sorrow and defeat, sought out religion as an escape, giving rise to the new power in King's Landing, the High Sparrow.
The arrival of Winter adds another element, as food becomes scarce and battle becomes diffcult. Hard to say how this will play out until either Stannis THE MANNIS or Roose Bolton solidify the North.
Arya begins her training in earnest, further removing her from her identity. Of the remaning Starks, two are beyond the Wall and one is beyond the narrow sea, and all three are deeply ensconced in the magical/supernatural.
Sansa and Theon have a great scene. We get the reveal that Bran and Rickon are alive, a payoff that no one's known about since mid season two. It goes all the way back to Robb sending Theon as emissary to Balon for his "navy". The acting from both Sophie Turner and Alfie Allen is some of the best of the series.
Cersei is not yet completely broken, though her game has backfired horribly. We get some schadenfreude in her short scenes. Not only that but she already cast off her own lifeboat, having sent Jaime to Dorne, where is also captive.
Now, Hardhome.
The payoff between the the series' first scene and this is stupendous. We see the small girl from the first scene. We see the White Walker who sits ahorse and screeched at Sam at the end of Season Two. And we see the White Walker in Charge who converted Craster's baby into something inhuman.
It's not simply nonstop action for the sake of nonstop action, as was the Watchers on the Wall. It's about putting aside petty differences for the greater threat. It's the Wildlings trusting Thormund but not Jon, and that being good enough. It's the Thenns being a pain in the ass. It's those characters somehow raising the stakes even higher for us and making the ensuing battle mean something.
Plus you have the stuff that's simply cool. The giant. The White Walker walking through fire. Jon defeating one with Longclaw (one of two audible cheers this season from me. The other also involved Longclaw). The effects and the swordplay and the panic and the bravery.
The game of thrones has changed completely. It somehow doesn't matter what the high lords are doing in Kings Landing now.
The episode also speaks to something larger about the show in general. I've noted before it's difficult and silly to judge a show based on a single episode, but because shows (outside of Amazon and Netflix streaming shows) air on a weekly/episodic basis, it's the way we talk about them. But in speaking about the show at large, one cannot do anything but look at the whole picture of a season. In ten episodes, with many storylines, the season follows with Introductions (episodes 1-2) Rising action (3-7) Climax (8-9) Denouement and leading into the next season's storylines (10). So, to judge, for example, episode 4 as being slow compared to episode 8 is silly. Episode 4 does what episode 4 is supposed to do and episode 8 does what episode 8 is supposed to do. That of course doesn't mean it's not interesting, only that it's interesting in a different way.
So when speaking to teh qualify of a show, it's impossible to make a judgement until all the bets are in.