Daniel LaRusso: You're the best friend I ever had.
Nariyoshi Miyagi: You... pretty okay too.

— The Karate Kid (1984)

Works with their own pages:

In General

Miyagi and Daniel's entire relationship, especially when you take their backstories into account. Daniel lost his father seemingly not long before the trilogy began, and Miyagi lost his wife and son while he was serving in World War II, so the two of them essentially are the family to each other that they couldn't have.
- Miyagi's pet nickname for Daniel is Daniel-san, with "-san" meaning "Mister/Miss" and making it a honorific gesture. In the contextual meaning it represents Miyagi's teasing affection for him.
- Easy to miss but Miyagi's Japanese grunts and gestures are often subtle Bilingual Bonus moments which shows that Miyagi treated Daniel more like a child rather than a teenager. Given Miyagi's past and the chemistry both characters have, it makes it for the audience clear when Miyagi started to open up to Daniel.

They're both horrible people, but Kreese and Silver's Villainous Friendship is full of this. Especially in the beginning when Kreese has hit rock-bottom and goes to Silver with all his problems, Silver sends his friend on a vacation and promises to help with his revenge after he's recovered.
A blink-and-you'll-miss-it moment in the third film (which overlaps with Tearjerker). Miyagi takes out a picture of himself and Daniel, who has been drifting away from him lately and has confessed that he feels 'confused.' Miyagi looks at the photo and softly utters two lines:
Miyagi: Hope confusion end soon, Daniel-san. Miyagi heart empty without you.
Miyagi preparing a healing foot bath for Daniel, after Daniel wounds his big toe (when secretly training with Terry Silver). While Miyagi is unaware of what Daniel is up to, he knows that Daniel is hurt, and still provides help to him no matter what.
Jessica forgiving Daniel after he breaks a guy's nose for harassing her in a dance club, with her telling him that she's still his friend, gives him a kiss on the cheek and encourages him to try to make amends with Mr. Miyagi.
Miyagi's Big Damn Heroes moment. He is full of Tranquil Fury, and shows that he will protect his student, no matter what.
The ending of the film, where Daniel hugs Miyagi happily. Also, before the final round, Daniel makes a point of bowing to Miyagi out of respect, and as an apology for being at odds with him during the event of the movie; Miyagi bows in return.

After she tries to kill a cockroach, Julie makes amends by showing one of the monks a grasshopper she's holding. The monk gently places it in a tree, and they smile at each other.
One evening, Julie starts playing music on her radio and accompanies it with a kata. Then the monks come in, and instead of telling her off, they join her!
The monks going to the trouble of making Julie a birthday cake, singing "Happy Birthday" to her, showing her Zen Archery, and granting her wish of coming to visit.
Miyagi waltzing with Julie, and later his pride at seeing her all grown up.
- Julie, after learning to dance from Mr. Miyagi, tells him:
Julie: It's too bad you never had a daughter, Mr. Miyagi, you would have been a good parent.