The casual Relationship Upgrade Hori does when she tells her father that she and Miyamura are dating. By that point, he'd been practically part of her family anyway.
In chapter 37, Souta is worried that he'll lose Hori to Miyamura. Miyamura reassures him that his "big sister" will always belong to him, but asks to have "Kyouko" in return. Miyamura then says that he will be Souta's "big brother," to which Souta agrees to both.
Really, any moment with Souta counts. He's a lovable little kid who very much appreciates having Miyamura around.
Remi and Sakura's friendship. One is the school "princess" and very cute, and the other's a plainish, hardworking girl. The two look out for each other and envy each other's strengths nonetheless, and they've always got each other's backs.
Sengoku and Remi's relationship as well. Sengoku had never been the strongest of men, and he's easily frightened by bugs and the sight of Hori, but having Remi around makes him want to protect her. Remi feels the same about him— since he's facing all the things he doesn't like when trying to be strong for her, she appreciates all that he does.
Heck, the whole student council trio are great friends. They really care for one another and try their hardest for one another.
One of Miyamura's childhood bullies, Makio Tanihara, ends up feeling incredible guilt after the fact and wanted to make amends. Miyamura meanwhile is starting to warm up to the idea of making friends with his former tormentors. So imagine his surprise when he runs into Tanihara outside his bakery while he's working. The two aren't able to talk about the issues directly, but he is able to order some food from him after telling him that he heard the food there was alright and getting Miyamura's helpful recommendations.
The chapter that reveals how Remi and Sengoku started dating. He ended up lending a lot of books to her, and they kept trading off until the day he asked her to visit his house for more of them. He ends up confessing to her after she asks him what he'd do if the world ended the next day.
Despite knowing that she's very popular amongst her classmates (especially the boys), Remi isn't close with anyone because she knows they all look down on Sakura. The reason she becomes interested in Sengoku is that he treats both her and Sakura as equals while having a conversation about books.
After Yuki finds out that Sakura confessed to Tooru, he tells her later that he turned her down and said he was dating Yuki. She's confused by the gesture, seeing that they're under no obligation to continue fake-dating and seems obviously insecure about the whole thing. But he tells her that it's alright with seasonal metaphors— that "snow" doesn't have to melt just because the "cherry blossoms" arrived.
"How about we get married?" And said on Christmas, to boot. For anyone who's read the original webcomic, you'd know that this does come to pass, and they have a little boy together.
The entirety of chapter 81, where Miyamura and Hori describe how they view each other.
Iura's Big Brother Instinct kicking in when he learns his sister wants to study and get into a good high school but was laughed at. In general, when Iura gets a chance to be a proper friend and brother, it tugs heartstrings. This scene was also thought to be responsible for Iura shooting up to third place in the official character poll.
Chapter 98's cold opening has Souta showing off a school paper he got a good grade on to his family. The subject matter was of a family matter, and Souta decides to write about Miyamura. Doubles as a funny moment because the rest of the family is completely flabbergasted that Souta wrote nothing about them.
Hori-san to Miyamura-kun
In the first part of chapter 173, Ishikawa and Yanagi find a girl whose skirt got caught in the train doors. They help her out by standing next to her so that no one can look up her skirt. The girl is touched by this kind gesture and asks Ishikawa to be her boyfriend the next day. Ishikawa politely rejects her, stating that he likes someone else.
The webcomic's original Valentine's chapter had Sakura come up to Yuki and give her chocolates she meant to spread around. Taking a look into the bag, she obviously made some for Tooru, but right next to them are chocolates for Yuki too. At that point, Yuki attempts to get on a First-Name Basis with her.
Their improving relationship in the comic in general is nice. By graduation, Sakura admits that she liked Tooru a lot, but she liked spending time with Yuki just as much.