It's a shoujo romance. It portrays the feelings of love extremely well, the characters are likeable and I enjoyed the show very much. It's sweet. It only has two significant problems, although I'll be raising a few minor niggles too.
(a) It has a habit of resolving things a bit too easily and quickly. Antagonistic people are won over without enough effort. I wonder if it hasn't been over-condensed from the manga?
(b) The happy couple appear to be aged 18 (Nike Lemercier) and 12 (King Livius I).
If the show were gender-swapped, it would be unwatchable. Imagine a romantic series aimed at a male audience, with an adult man marrying a twelve-year-old girl. It would look predatory. You'd be screaming and fleeing. I think the actual show gets away with it, because both the target audience and the older half of the romance are female and there's clearly no question of any sex happening until Livius is older. However it's still a full-blooded love story, including one big kiss that leaves both parties hot and flustered. If you think it's squicky, you're not alone.
I should also qualify that "18 and 12" thing. The anime never tells us anyone's age, so it's just whatever you want it to be. The manga retcons itself. Livius is fifteen until chapter 40, when he's suddenly twelve. Nike in the manga meanwhile looks childlike and hardly much older than him, although the anime makes her look older. I'd have guessed eighteen. Maybe she's just a mature-looking fifteen? However you cut it, though, Livius only comes up to her shoulder.
I should summarise the story. Nike is a princess from Rainland, a poor country that only still exists because Sunland couldn't be bothered to conquer it. Nike's also not ladylike. She's the kind of princess who's always had to peel potatoes, cut wood and make her voice heard above three elder siblings. She's a lovely girl, but to stop her doing what she wanted, you'd have to nail her to the ground.
King Livius I of Sunland, meanwhile, is a precocious and occasionally sinister brat who conquered the known world in three years. On meeting his new bride, he throws her in prison. However he's also lonely, having lost the only person he was close to (his mother) when she was assassinated.
It's a historical/fantasy setting. Nike knows weather-controlling magic, which is mostly rain. I guessed a 16th century tech level from ep.1, but it's probably more like the 18th. There are enemies at court, people who lost out in Livius's political reforms and so on. All that I liked. Rainland has similarities with old Japan, not least in the policies implemented long ago by Nike's all-powerful grandma, so you could perhaps try to read an East-West metaphor into the series. Interestingly, that Tokugawa-like grandma can be both sympathetic and villainous. Rainland's also way above Sunland in both magic (weather control) and tech level (the idol concert, although that's probably just the anime being silly), despite being impoverished, insignificant bumpkins.
The show's also funny. Nike and her sisters can all be a hoot, with Nike not inclined to suffer quietly when it comes to things like corsets.
The writing's quite intelligent, although it does have familiar story elements (e.g. would-be rivals) and that problem I mentioned of challenges not being followed through properly. Livius starts thawing almost immediately, with no effort from Nike. Ep.5 has a villainous priest see the light so readily that it's almost bathos. I like the argument that this is basically a series with no villains, only people who haven't realised that they could be friends, but those developments would still have been more satisfying if our heroes had had to work harder for them. I'm going to hope that this is adaptation mis-compression and that it's done properly in the manga.
Nonetheless the character work is quite good. The show's title is important, representing the most important thing Nike has to teach Livius. He's forgotten what beauty is. "The world just exists to hurt people and be conquered." The Nike-Livius romance is analysed and challenged. "Are you going to become his mother?"
I liked the show. For me the age thing was a bit of a block on the romance, but it is chaste and well done. However I have a few minor niggles.
The would-be rapists in ep.1 are unnecessary and silly.
I disliked Nike's rain-summoning song. The Engrish is jarring, not because the pronunciation's overly bad but because the not-very-good singer isn't getting that much from the lyrics even when she's singing in Japanese. Her rendition of "it's a tender rain" almost never has tenderness. It also sounds more J-Poppy than I'd have liked, especially with drums in the background. Wouldn't something more magical and mystical have been better? (It's not a horrible song, though, and some people like it.)
Oh, and Livius's actor clearly has a man's voice, not a boy's. This may or may not reduce the creep factor for you.
This show isn't all it could have been. I think another four episodes could have made all the difference, to flesh out the character development and make sure that the show properly earns all of its changes. More fundamentally, there's also the alienating premise. However the Nike-Livius love story is sincere, well told (apart from some elision early on), funny and charming. He learns how to read her emotions from the characteristics of the rain she makes, for instance. It's too flawed to recommend easily, I think, but there's a lot to like here.