Everything from Vyse giving Ramirez a traditional air pirate send-off, the scenes depicting life returning to normal throughout Arcadia, to the music that plays during the end credits, and final scene of Vyse's new ship on its maiden voyage sailing of toward the horizon. It all feels like a fitting end to a memorable journey.
Enrique's quasi-familial relationship with Gregorio, to the point where he refers to Gregorio as an uncle. The goodbye they share is a mix of heartwarming and tearjerking. It really shows that in spite of Enrique's passionate feelings towards Valua's brutality, he's still able to make an honest attempt at discerning between the brutal and those facing pressure from the truly brutal, having to make tough decisions against their will.
Gregorio: Prince Enrique. Is there anything I can do to make you reconsider?
Enrique: ...No... I've made up my mind. I am not going back to Valua. I know that you've noticed a change in the Empire as well... They are headed down a dark path... Trying to rule the world with an iron fist... It will be Valua's downfall... This world... this sky... is not Valua's to rule. It belongs to the people... And to right the wrongs that Valua has committed, I have decided to travel with Vyse and his companions. Tell that to my mother. And also that I pray every day for her good health. This is goodbye... I must go. Be well.
Gregorio: Farewell, Young Prince.
The fact that they're both standing on separate ship decks while having this speech symbolizes the divide between them.
The Moonfish/Piccolo/Moon Hamachou Sidequest, where you find moonfish around the world for the strange pet bird of Maria. For even a long-term fetch quest, there's a lot of benefits for doing it (the rare item rewards, learning of the backstory behind the Doctor, Ramirez, and Maria's family, continuing Piastol's sidequest, and obtaining one of the final discoveries), but most importantly, you're helping a traumatized orphan out of depression, and her interactions with Vyse and Piccolo (her pet) are adorable. After this sidequest, you can fight Piastol for the fourth and final time. Vyse then tells her that her little sister Maria is alive and that she should see her. Their reunion tops off these sidequests perfectly.
The conversations Vyse has with Aika and Fina right before the final confrontation with Galcian. It's really driven home how much these three care about each other if you play it in-character for Vyse, ending on an adorable one-armed hug with Fina and kiss on the cheek from Aika. Three true friends about to take on the greatest threat to free civilization the world has faced since the Old World - what could be better or more precious?