I don't want to speak on the romance aspect of the movie because it was very subtle and I need to watch it again to understand it.
But I just wanted to say how much I like Rikako as a character. I know people really dislike her and I can't argue against that, but I see her violence more of a reflection of the past and choose to ignore it as it was something the creators probably didn't think too much about. She pushes people away because she's hurt. These days she'd probably just shove him to showcase the emotional distance between the two.
I like headstrong characters and I do love *****y female characters that eventually calm down but never lose their fire inside. That's just my preference, I like characters who take action and formed their own opinion. So I really liked it when Rikako never changed her opinion about the new town. She doesn't like it because she doesn't feel comfortable in a close-knitted community. She doesn't want to have to do things just because a small community expects her to do them. People don't like her attitude, but she just keeps to herself and studies so that she can move back and be accepted into a good college in a busy city where she feels at home. When she loaned money from Taku I definitely expected that to turn into a conflict, but she just saved up to fly home for once and she knew that her father would give her some money out of guilt. Yet she still wanted to see him because she loves him.
And I also do like the romance, the scene of Taku understanding why Rikako loves Tokyo and agreeing with it is still in my mind. They seek out the same future, which is not true for either Rikako and Yutaka or even Taku and Yutaka. Yutaka does influence Taku and he considers other big cities, but he still carries that stubborn vulnerable girl in his heart because he just likes her. There's nothing more to it, he was attracted to her (shown through the beach pic he bought) and he understood and supported her ideas and feelings. As I said I need to rewatch it to get a better idea of the subtle romance, but from what I remember I can definitely see how they gravitate towards each other without being able to say something. I've seen that there are videos about Taku being queer and having had feelings for Yutaka, but ultimately dismissing them in favor for a straight relationship he feels more comfortable in, but I didn't really notice it on my first watch. I paid attention to his relation to Yutaka, but I also thought the movie wasn't about Taku forming a romantic relationship with a female classmate. His interest in Rikako seemed genuine enough to me, but I'm not saying that there isn't an indication of him being bi and having considered a relationship with Yutaka.
It's definitely something I need to pay closer attention to on a second watch. The movie is incredibly subtle, but I just love coming of age stories. Normally I'm not that into romance stories, but Studio Ghibli and animes like Toradora really made me appreciate well-written love stories. I wanted more from this movie, more story to see them fall in love, but I see the point of not showing everything. At first I thought I dislike this movie, but after thinking about it a lot I really love it actually.