There's more to the story than that!
How about anime that has a significant plot and a sprinkle of romance on top of it? Hm? Like the sound of that?
Great, because we also love that.
Sometimes the shows that are straight-up romance feel a bit dull and boring, and the characters in them seem unrealistically devoted to this one and only task at their hand: to deal with their love life. But if the characters have some non-romantic goal in their life and in the process deal with some sort of relationship, then it becomes more interesting: the characters have some initial depth that makes them more humane. And we've got a list of shows like that.
Sword Art Online (1st Season)
Hear us out: the first season of SAO is good. It feels too repetitive and harem-y later on, and Kirito becomes too overpowered as the story progresses, but the first season isolated from everything that came after that is a good story about the character development in a harsh world and the blooming romance, one that doesn't feel too rushed and too out of touch. Sure, there's a hint of desperation here, but the relationship between Kirito and Asuna is a good addition to the whole plot.
Fruits Basket
On one hand, it's one of the most popular reverse harems in the history of anime. On the other hand, it's so much more than that. The story mostly concentrates on familial bonds, on the problems that arise from being who you are, from accepting yourself, or, on the contrary, fighting who you are. It focuses first on creating proper characters, ones that you can bond with, and then gets into the romance territory. This is the reason why the viewers get so enamored with this show: the characters are diverse and likable, fully-fledged and deeply broken.
Cross Game
It's a sports anime first and romance second. Yes, it mostly focuses on baseball: it's the thing that connects two titular characters of the show, who have something akin to a cat and dog relationship. But over time through baseball, they connect and develop and learn a lot of things about themselves, ones that are not related to their love life but to their overall worldview.
Katanagatari
The pair of characters embark on an adventure, and romance blooms in the process, but the adventure comes first. This anime is packed with action and dialogues, as dialogues sometimes replace the fights. It tells the stories of why people fight and progresses through the meetings with the side characters. And it has a lot of special humor packed with deliberately failed attempts at being funny.
Full Metal Panic!
The romantic plot here is so substantial that romance is not even listed in the genres — but it's here, and it's good. It fits the overall narrative of mecha comedy, filled with conspiracies and battles and attempts to fit in. This mix of a serious militaristic mecha with high school comedy is what makes it interesting, and the romance that is apparent in the second part also adds a bit to the pot.
Chivalry Of The Failed Knight (Rakudai Kishi no Cavalry)
This mix of school setting with action and fantasy has some ecchi elements: it's about kids who can shape their souls into weapons and who study in the special school to do so. It seems pretty basic and boring at first sight, but in reality, it subverts the tropes you'd usually see in light novel adaptations and in general uses the tried-and-true schemes in a refreshing way. And that also can be applied to a romantic part of the story, one that follows the relationship of a failure and a tsundere.
Toilet Bound Hanako-kun (Jibaku Shounen Hanako-kun)
Don't be scared by the word "Toilet" in the title: it's merely a place that the ghost of Hanako-kun is bound to. The main character of the show, Nana, wants some romance in her life, but instead encounters a ghost boy who tries to help her but has his own story. And this show focuses more on the character development and its mysterious aspect, one that brings a lot of comedy, and on the failed attempts at romance. Nana views the status of the girlfriend as something that she should obtain because that's what people do, but the boys she presumably likes don't actually interest her at all — she doesn't even remember their names. So it's a show that makes a joke out of romance.
Planetes
The visuals in this anime are stunning. The story is heart-wrenching and heartwarming. It has a lot of action, a lot of drama, and a significant portion of romance. It's slow-paced and introduces all the characters to the viewer before they get into some meaningful action, and without that introspection, the finale wouldn't hit as hard. Then again, it's a show about garbage collectors in space. It's bound to be weird and slow. And that applies to the romantic part of it, too.
Guilty Crown
Japan is controlled by the US because of the virus outbreak. Not everybody likes it, so the resistance has been formed, and the story follows the people who got accidentally dragged into the liberation war. The plot sometimes seems like it tries to deal with too many themes at the same time, including the romance between the two main characters, a shy high schooler who got overpowered and an idol. And this mix sometimes feels comedic with no intention to be like that. It's a wild ride, but the romance fits in here well without taking too much screen time.