There are scenes in the very first two episodes of Season 1 that foreshadow aspects of the ending. When Ned Stark beheads the deserter in King Robert's name and says "rightful King of the Andals and First Men", the camera cuts to Jon, who is the rightful King, and Bran, who will actually be crowned King after him. Likewise, the conversation between "Kingslayer" Jaime Lannister and Jon about Jon joining the Night's Watch and the oddly prominent handshake between them. That was Jaime marking Jon as one who'd commit the very same crime with the Mad King's daughter, no less, and be forced to (re)join the Night's Watch because of it.
The influence of Lord of the Rings goes beyond the reveal of Archmaester Ebrose's "A Song of Ice and Fire" history book, it actually extends to the endings that the four Stark children get.
Jon Snow's ending takes after Samwise, Merry, and Pippin, getting to be the respected leader of a group of otherwise rustic people (Hobbits for Sam, Free Folk for Jon) far from the wars and politics of the rest of the world.
Arya Stark's ending, sailing off into the unknown west of Westeros is strongly similar to that of Frodo, Bilbo, and Gandalf (later joined by Sam), who sailed West to the Undying Lands.
Bran Stark is crowned King in what takes both after Aragorn's coronation and the Kneel Before Frodo moment that followed.
Sansa Stark is crowned Queen in the North in an ending that is closest to Aragorn's (minus the marriage). Her crown even somewhat resembles the Elvish diadems and circlets that Legolas, Arwen, and Elrond wear to Aragorn's coronation.
Jon Snow's actions in the final episode, where he abandons Castle Black and heads back into the Far North with the surviving Free Folk makes perfect sense; there is no Night's Watch anymore, it doesn't exist as a formal organization and with the White Walkers and the Night King destroyed, there's no point to its existence, either. Especially since there's a giant hole blown in the eastern expanse of the Wall! Jon Snow's "punishment" was, effectively, an excuse to "exile" him to the Far North for the remainder of his life — the Essosi wouldn't know that Jon didn't view it as a punishment, the Northerners didn't care that it wasn't actually punishing him (since they wanted him free in the first place), and the Six Kingdoms' denizens neither knew nor care. And Jon? He knew he was being given an opportunity to do what he really wanted; leave the Seven Kingdoms and all of their bad memories behind to instead lose himself in the place where he first learned to be happy and free with the Wildlings.
Another layer of brilliance: Jon's loyalists intentionally trick Grey Worm and his supporters into sending Jon to the Wall, knowing full well that he can escape to beyond it at any time. The reason why recruits didn't escape to beyond the Wall before was that they would be killed by the Wildlings or worse, but now that the Wildlings are friendlier to southerners and the White Walkers are no more, anyone sentenced to the Wall can desert and live a Wildling life.
At this point, Beyond the Wall is likely the safest and healthiest place for Jon to be, too. Tormund and the Wildlings are fiercely loyal to him, none of them care about Jon's titles or parentage, and Jon's about as far removed from the South and Essos as he can possibly get. Moreso than any of the other Starks, Jon is at his happiest far away from the political games they play in the Seven Kingdoms.
With the North an independent kingdom, Jon is effectively free to return to Winterfell whenever he wants. The South can't do anything about it, and Daenerys' forces have already left. The entire idea of exiling Jon was just a smokescreen to get the Unsullied to leave.
The Starks all spend years trying to reunite and now that they have and all their wars are won they all ended up choosing to go their own way and separate.
Sansa was chosen/chose to be Queen in the North
Bran likewise did the same and King of the Six Kingdoms
Arya decided to leave Westeros and explore the unknown west of the world
Jon was the only one unable to truly choose and was forced into exile at or North of the Wall...But then again, Jon is "Not a Stark".
That blade of grass being pointedly focused on as the Free Folk emerge back into the Far North is dripping with this:
Firstly, it's long been implied that the Far North wasn't naturally cold, but instead trapped in an unnatural eternal winter by the cursed presence of the Night King and his White Walkers. Well, they're dead now. So of course the curse is broken, which means the Far North (and probably by extension the Lower North) will be warming up to a much more reasonable set of seasonal weather.
Secondly, it Book-Ends the entire series. We started with the knowledge that "Winter Is Coming". Well, what does that grass signify? "Spring Is Coming."
Of course, the assembled lords and ladies laughed down Samwell Tarly's suggestion for a democratic system, but then agreed to replace the hereditary monarchy with a system of elected kings from their own ranks. Westeros has been a feudal hereditary monarchy for thousands of years; simply listening to the smallfolk is going to sound like craziness at first glance. But agreeing to vote for an elected king from their own ranks? That makes more sense to them, because it's still leaving the power where they presume it belongs. Plus, it's not entirely unprecedented; a similar process was used in the past to resolve issues of unclear succession, in the so-called Great Councils of the Targaryen dynasty. Maybe this will even set a good precedent of power-sharing that might, over time, trickle down to include commoners as well.
There is also another issue with the commoners having the vote. In the modern age, we have the technology to communicate all other the world, making it easy for an election to happen in a day. Depending on the plot, it can take anywhere between weeks and months to travel from north to south. In the medieval-esque times Game of Thrones was set in, it would not be efficient to run a proper electoral system, given Bran, Tyrion, and Sam imply it's time to start improving technology.
Despite losing her way, in the end Daenerys did end up "smashing the wheel" as she claimed she intended. Her actions demonstrated to everyone just how dangerous a single person with such unchecked power could be, while her death left a power vacuum, giving the remaining Lords the chance to reform the government into an Elective Monarchy, thereby preventing unfit rulers from rising to power.
While it does make them Karma Houdinis it makes sense that no one wanted to punish Grey Worm and the Unsullied for their war crimes. Between the War of the Five Kings, the war between Dany and Cersei, and the battle with the White Walkers, the Seven Kingdoms likely are lacking in armies right now, and the Unsullied are already above average soldiers, so letting them get away with what they did was likely the lesser of two evils than going to yet another war. It's likely that them leaving was the best case scenario.
Given that the Northern soldiers and the Dothraki were also guilty of war crimes as the last episode graphically demonstrated, punishing the Unsullied while letting the others get away scot-free would be a blatant double standard and be sure to invite retaliation from the Unsullied. Letting them go was the only way to stop things from descending into mass bloodshed once again.
Then again, who is really innocent anymore?
Why did Drogon not avenge his mother? Even with the Targaryen blood, Jon had just murdered the one being he had known and trusted his entire life. Yet even though dragons are amazingly intuitive, they're still animals, and Drogon never actually saw the deed take place. His mother had (tragically) trusted Jon with her life, and had encouraged him and his sibling to do the same: he simply failed to perceive Jon as the killer.
Daenerys died for the same reason that Drogon didn't avenge her — she was incapable of seeing him as a potential murderer because she saw him as a fellow Targaryen rather than a Stark. To her, the threat was from how others perceived Jon rather than from Jon himself. The possibility that Jon was even capable of killing her out of love from anyone else would never have crossed her mind.
Going further, Daenerys never had a proper family — Viserys was abusive, Khal Drogo was abusive before he came to love her, and advisors and close subordinates like Jorah, Daario, Grey Worm, Missandei, Barristan, and Tyrion were simply never her equals or her family, no matter how much they loved her or she loved them. Her dragon children gave her love and affection but not in human terms. She never had any unconditional love for any human being (possibly apart from Jon) so she couldn't conceive of being able to love anyone else. Even if he was raised as a bastard, Jon still loved his adopted Stark family unconditionally and it was the sort of love Dany never really knew. So, Jon "betrayed her for love" — the love of his family, the sort of love Dany couldn't have really known about or understood due to her upbringing.
After all the complaints about the Night King's lack of motivation for being so obsessed with killing Bran in particular, he turns out to be the lynchpin for the whole world moving away from destructive absolute monarchies and hopefully one day leaving them behind entirely and replaced with something harder for the walkers to fight, which he was likely able to see with the same powers as his opposite the Three-Eyed Raven.
Bronn wanting to fund the rebuilding of brothels rather than ships. As the last Master of Coin pointed out in the novels, they're a more reliable investment (prostitutes don't sink, and when pirates board them they pay like everyone else). Plus, as Cersei pointed out (when asked to ban brothels by the Faith Militant), a lack of brothels would only cause sailors to take their trade elsewhere.
Tyrion isn't mentioned at all in the annals of the Westerosi civil wars because Archmaester Ebrose heard that he had been snubbed for the position of Grand Maester by the Hand of the King in favor of Samwell Tarly, who hadn't even finished his training yet.
Additionally, Archmaester Ebrose was writing the histories while the Kingdoms were being run by the Lannisters. As he was writing it, Tyrion's achievements were either being downplayed, or outright erased.
Considering most people believe Tyrions role in the story is that he was the Evil Chancellor to a terrible king, murdered his king and his father in cold blood, went to Essos, and came back to Westeros with the woman who would destroy Kings Landing, he might have believed he was being charitable by leaving Tyrion out.
Arya setting sail for the uncharted west appeals to her lust for adventure, but it probably helps that it will take her ever-further away from Braavos in the east, in case the Faceless Men ever decide that a non-FM running around with FM training is too much of a security risk and come after her again.
On a meta level, there are people concerned about Sam and Gilly's relationship, since he has become Grand Maester and Maesters are supposed to be celibate. But if you look at Sam's maester's chain, it only has a handful of proper links in it (an apprentice becomes a Maester when he has forged enough links to wear his chain like a necklace) and is held up by a normal chain. Sam isn't a proper Maester, he simply occupies the position of Grand Maester (the King's chief academic advisor), either by will of the King or as a political move by the Citadel to curry favor with the new regime.
It's also not like all the Maesters keep their vow. We see Pycelle with prostitutes multiple times on the show, and we can guess he is far from the only one. More than likely it would just be overlooked for Sam to have a mistress and child even if he were a full Maester.
"When you play the game of thrones, you win or you die" turns out to be true: every major character who actually played the game (i.e., sought power) winds up dead except Sansa, who wins by becoming Queen in the North. Bran, who winds up King of the Six Kingdoms, and Jon, who winds up (effectively) King Beyond the Wall, never sought power.
It's likely that most if not all of the large animals beyond the Wall have been killed by the White Walkers. The Wildlings are going to find themselves in a food shortage very soon if they don't find an alternative source of substance.
There are also a lot fewer Wildlings to feed, and with warmer weather and a giant hole in the Wall there will probably be recolonizing of not just beyond the Wall, but the North itself from southern lands.
Still a Fridge Horror in terms of the damage the loss of so many species is going to do to the North's ecosystem.
Drogon is still on the loose and will inevitably become a threat unless Bran is able to find or somehow control him with his powers. Even if he can there is no telling how much damage the Dragon might cause before then.
Daenerys's control over the former slaver cities of Essos depended on the nobles fearing her and her dragons. The series ends with Daenerys dead, as well as two of her dragons, and Drogon has flown away to parts unknown. Her army of Unsullied and Dothraki are both weakened and seemingly have no intention of returning to their homeland. For all intents and purposes, the Masters of Slaver's Bay are free to try and overthrow Daario and resume their cruel practices without fear of reprisal.
That's if they're still alive. Daario once suggested to Daenerys that she kill all the nobles back in Meereen. With nobody policing him, Daario probably eradicated the nobles already to prevent another revolt.
The Masters probably revolted the moment Daenerys left. She left three barely stable cities under one man with skewed morals and no experience in ruling. It's doubtful that that went well.
The Night's Watch was underfunded and undermanned even when they had an important role. How wretched they are going to become now that they have no good reason to still exist?
Of course, that's presuming that Westeros actually means to revive the Night's Watch, as opposed to just making it up in order to bluff Grey Worm and his Unsullied into handing them back Jon Snow, who would then be allowed to slip away quietly into the wilderness Beyond the Wall, where he'd rather be.
That would be a rather elaborate deception, given that men in Night's Watch uniform came for him and were manning the Wall.
Or Wildlings dressed as Night's Watchmen, informed by Bran, who already knew the future, came to collect Jon, and then just kept using the clothes because they were in decent condition.
The Night's Watch just received the greatest advertisement they could have asked for — an actual invasion by the White Walkers. Sure, the Night King was killed and the Army of the Dead crumbled, but can one be sure there's nothing ELSE beyond the Wall? The Watch was underfunded as everyone thought they were guarding against mythical beings, a refuge for the unwanted, but now they've been vindicated and, at least in the North, respected as an organization. They can likely expect a renewed amount of funding and personnel.
They are vindicated and rendered obsolete at the same time. They are vindicated as guardians of the living, sure, but what are they guarding the living against now? People know of nothing else beyond the wall, so the current Night Watch is still as good as guarding the realm against mythical beings. The only thing left that might be out there that everyone knows about is the Children of the Forest, but Bran probably tells everyone about how they are or about to be extinct because it's essential to his story. The awareness of the WW probably won't help much, because it's already proven that Southern Lords don't care about the Wall when the WW has already breached it. The only reason left for the NW to exist is as a glorified penal colony and dumping ground for unwanted people, which is no good reason.
There's also a massive hole in the Wall now that wasn't there before, necessitating men be there to guard it. One has to remember that as friendly as Tormund and Jon are, the people of Westeros still see the Wildlings as barely-human barbarian savages and can't expect any peace with them to last any real length of time. Aside from that, well, for hundreds of years at least, no one thought the Night's Watch was actually necessary; people in the North thought the White Walkers were long extinct, people in the South thought they never existed, and no one actually considered the Wildlings much of a real threat to the realm — Mance Rayder's army was only a threat because Robb had taken the northern forces south, and would have crumbled against real opposition, as demonstrated by Stannis. The Night's Watch existed for hundreds of years under the pretense of protecting the realm from threats from the Far North, but in actual practice, existed as a convenient place to send unwanted sons, bastards, and criminals who were politically inconvenient to execute. The fact that the pretenses for the Night's Watch's existence are a lot weaker now don't remove it's practical application as a penal colony and exile.
The Wildlings would be lucky to even be numbered in two thousand at this point, and most of them would be women and children, and that is assuming most Wildlings go back to beyond the wall instead of just staying south. Of the five thousand who originally escaped Hardhome, the Battle of the Bastards probably kill a ton, then there's the fall of Eastwatch where a lot of wildlings were in the collapsing section, and there's the Battle of Ice and Fire which probably kills half of what's left. It would definitely take hundreds if not thousands of year for the Wildlings to regain their pre-White Walker number. Wildlings are only dangerous because of their huge number. Without that, they are no better than the Hill tribes, which Westeros has lived with for thousands of years without a wall. Peace with them would last for a very long time. The fact that the Night Watch still have a practical use as a penal colony is no proof that their condition won't deteriorate. The simple fact of the matter is that lords were unwilling to donate to the Watch even when they had a quantifiable enemy beating down the door. How much are people willing to donate when all the Watch does now is housing a bunch of criminals and letting them sitting around doing nothing?
Drogon takes Dany's body with him as he flies off. He is last spotted flying east towards Volantis. What lies in the east? The Red Priests, who have been shown capable of bringing people back from the dead, and hailed Dany as a messiah before...
One red priestess hailed her as a messiah and that was before she murdered hundreds of thousands of people. Daenerys is likely dead and staying dead.
More of a Fridge Tearjerker, but Drogon has lost absolutely everybody. His brothers and now his mother are gone. And if THAT isn't enough to make him feel alone, he is the last dragon in the world. His solitude is likely lasting until the day he dies.
As the dragons seem to have a level of intelligence approaching humans, this means that Drogon himself could go over the edge, and start taking out his pain on the humans of the world. And as repeatedly shown, there's very little, if anything, that can be done to stop him.
It's even worse considering a dragon's natural lifespan can be measured in centuries. Drogon's going to be lonely for a long time.
On the other hand, the literature suggests dragons are hermaphrodites, so Drogon could produce eggs. Which could lead to its own Fridge Horror.
In the War for the Dawn, both the Old Gods and the Lord of Light made their existence known while the Seven had no involvement. This leads to the question of what will happen to Westeros as many followers of the Seven convert to gods who they now know are real as opposed to gods who are either apathetic or nonexistent. Does this lay the groundwork for a holy war as the Faith of the Seven, who have a long history of reacting violently to anything that goes against their teachings, clash against the new religions growing in the continent?
It's unlikely there's much fight left in the Faith of the Seven. The High Septon/Sparrow and most of the fanatical Faith Militant died when Cersei immolated the Great Sept of Baelor. If there was anyone left who cared they would probably have come for Cersei in the immediate aftermath of that event.
True, but if a lot of people start converting to a new religion, that might revive the Faith Militant as part of a backlash. Particularly when Bran is so linked to the Old Gods (plus, his family followed them to begin with, aside from Catelyn Stark).
This video  notes that the Starks splitting into two branches (the North and South) parallels the Plantagenets, whose conflict led to the Wars of the Roses, a major inspiration for the books, then the TV series. Bran can't have children, true, but what if Arya at some point does and her descendants are at odds with Sansa's? A closer parallel of those wars might take place.
The elaborate new rules of succession sound good, but won't change anything in the long run. At the very least, several existent problems remain:
Euron Greyjoy razed what was left of the Iron Islands to make his new fleet, which Dany destroyed. Yara's partial fleet had fled before then, but their homeland — previously inhospitable — isn't going to have much to support life at this point. The Ironborn are going to need some alternative to raiding, fast, or else we're right back to war.
The Houses are hurting in general: House Stark is seceding and depleted of troops; House Greyjoy is essentially homeless; House Lannister out of cash; and Houses Baratheon and Arryn run by novices. While it's all but stated that Bronn is building a new house of his own, nobody's in any shape to fight any new threat. The first House to build a real army could potentially topple Bran with little resistance.
While the Iron Bank's best troops are dead, they still have their considerable resources. Without Drogon, Westeros is basically defenseless against the raw numbers the Iron Bank could throw at the kingdoms.