Jason meeting up with Thalia, his sister after they'd been separated for years. Bittersweet, though, in that he also finds out some pretty hard things about their mom.
Percy telling Frank he's proud to be related to him and later, Tyson calling Frank "brother" and Percy going along with it.
Frank entrusting his lifeline stick to Hazel.
Grandmother Zhang telling Frank that she's proud of him.
Any time Nico was being a big brother to Hazel.
Annabeth was hit pretty hard by Percy's disappearance, especially so soon after they'd finally gotten together. Piper being so sure that she and Jason were boyfriend and girlfriend probably didn't help. Then, mere pages into Son of Neptune, we find out that Annabeth was the only thing Percy remembered.
Percy giving up the Curse of Achilles, and the chance for a long, peaceful, safe life for the chance to find Annabeth.
Heck, any time Percy mentions Annabeth is undeniably heartwarming!
Percy wanting to protect New Rome partly because he wanted a life for him and Annabeth there.
Hazel recalling the best day of her life.
Percy's reaction to the arrival of the Argo II at the end of Son of Neptune.
Come on. Let me introduce you to my other family.
Annabeth visiting Sally Jackson at least once a week while Percy was missing.
And then on the way down, she whispers "I love you" into his ear, wanting them to be her last words. Aaaaaaawwwwww.
Sammy never forgot about Hazel, after all those years.
Piper, very relieved to see Leo, Hazel, and Frank after an attack on the Argo II and losing them in sea, spontaneously jumps off the ship and paddles towards Leo to give him a kiss on the cheek. It shows that Piper can be concern for the others as well. Could also count as a Ship Tease.
It's a small one, but Frank going to ask for Annebeth's help after getting trapped in the Chinese Finger Trap was pretty sweet seeing how he asked her because he trusted her to help and not tell anyone else.
Especially since ones a Greek and the other is a Roman and they've only known each other a few days
Hazel telling Frank he makes a very handsome elephant and then kissing him.
Percy and Annabeth's little date in Mark of Athena.
In House of Hades, Jason's protective instinct towards Nico after the revelation that he's gay (or bi, it was never specifically stated) and had a crush on Percy.
Jason telling Nico after the reveal: "Nico, I've seen a lot of brave things. But what you just did? That was maybe the bravest." Considering the stuff Jason's seen in his lifetime, that's saying something.
The fact that Jason realizes instantly why this is even a big deal to Nico when to the others it wouldn't even be worth batting an eyelash at. Nico's from the 1930s. Jason wasn't kidding when he said that letting that secret out was the bravest thing he'd ever seen. He gets how unthinkable that kind of reveal would have been in Nico's time without needing to be told.
And pretty much everything he says to Nico after the reveal. So completely free of judgement.
"If the others found out, you'd have that many more people to back you up, and to unleash the fury of the gods on anybody who gives you trouble."
"Dude! It's not like you've got a choice. It's just who you are."
Leo swearing on the River Styx to come back and get Calypso out of her prison. and he does!
Leo asking Calypso to weave a fireproof pouch to put Frank's firewood in so that Frank wouldn't have to worry about it catching fire anymore. It also shows just how far Frank and Leo have come as friends.
The moment everyone gets a chance to register that Percy and Annabeth are out of Tartarus. Jason gives Percy a big bear hug, and Piper hugs Annabeth and bursts into tears.
Nico flat-out tells Jason he doesn't like to be touched (although he does say "please"), yet still initiates affection with his half-sister Hazel, taking her hand or kissing her.
The two camps pledging mutual friendship and alliance. No more Greek-Roman divide!
Nico informing Frank that Frank still has plenty of time before that last bit of firewood burns out.
Percy and Annabeth's plans: they'll spend their senior year together in New York, then off to New Rome for four years of college under the protection of the Legion.
Annabeth: And after that... Well, Reyna and Frank said we could live in New Rome as long as we like.
Jason and Piper kissing on the roof of Zeus's cabin.
Jason: That night at the Wilderness School, our first kiss under the stars..."
Piper: The memory. The one that never happened.
Jason: Well, now it's real.
Coach Hedge showing off his brand-new boy to everyone from both camps.
Nico and Will flirting.
Heck all of Will's actions towards Nico, including refusing to let him risk his life shadow travelling and saying - somewhat snappishly - that other people do care about him.
Will: "Oh please. Nobody at Camp Half-Blood ever pushed you away. You have friends - at at least people who would like to be your friend."
Also Nico's clear acceptance that Percy is with Annabeth and is going to stay there. It's so... refreshing... to see someone just be willing to let a crush go instead of going Yandere.
On that same note, Piper and Reyna have nothing but the utmost respect and admiration for each other. When Reyna shouts a greeting as Piper and Jason enter the fight, Jason takes a minute to realize she's not talking to him, and Piper and Reyna fight side by side.
And, last but by no means least, the very last scene of the series: Leo is brought Back from the Dead, flies to Ogygia, and he and Calypso fly off into the proverbial sunset atop Festus the Ressurected Dragon.
To clarify: After the battle with Gaea Leo sacrifices himself, burning himself alive, shortly after which Festus injects him with the physician's cure, so he can be alive as he flies to Ogygia. The dude killed himself and brought himself back to life just so he could be with Calypso. It's about time.
Percy kisses Annabeth on the spot where Athena and Poseidon's rivalry first began.
Percy: The rivalry ends here. I love you, Wise Girl.
Hades is actually a sweet father to Nico. Honestly all the demigods relations with their parents in this book were cute.
Will and Nico's newfound friendship, along with a possible Ship Tease.
Leo's last words.
Leo: And by the way - I love you guys.
Nico's new friendships with Reyna and Jason. Especially Jason getting all excited about Nico deciding to stay at Camp.
Jason: Oh, man. Wait till I tell Piper. Hey, since I'm all alone in my cabin too, you and I can share a table at the dining hall. We can team up for capture the flag and sing-along contests and -
Nico: Are you trying to scare me away?
In the same scene, Jason wanting to hug him, actually remembering Nico doesn't like touching, and Nico accepting to make an exception!! When you remember the last interactions they'd had...
The very last chapter - Leo is Not Quite Dead. The first place he goes? To Calypso.