Short Version
Very, very good anime! You don't have to like music to be able to enjoy this, it is a prominent part, but there is much more to it.
Story
Overall, the story is amazing. It's very well paced (majority of the time) and it never creates pointless drama. The downside is when they show multiple performances, which is necessary for those parts of the anime (first and second season). I love the music, but it can get boring when they're talking about the preformances for minutes straight. They're usually pretty good with this, though. Keep in mind, I don't like music anime.
Animation
This is probably the anime's lowest point. Most of the time, it's a very good looking show and movement is well done. However, in unimportant scenes, it's very noticeable how lazy the animators got. It personally doesn't bother me too much, but they were simple mistakes that could have been fixed.
Sound
All the music is well done, and fits the scenes. I particularly like the music used for the previews. The performances are very well done.
Characters
The strongest point of the anime. This anime has the strongest character development that I've ever seen. Slowly, characters begin to change, you don't notice really, and then BAM, a scene comes where they do something you never would have expected them to do when they first came on the show. It's not surprising though, they've become a character who would do those things. There are big developments that change them too, of course. However, the subtle moments that make the characters grow is where the charm of Kono Oto Tomare! lies. Most of the new characters that come in, you will hate. By the time your done with the series, you'll love them, but it won't feel forced at all.
Conclusion
Again, I don't like music anime, but Kono Oto Tomare is my favorite anime. From it's subtle moments to it's action and tension packed performances, there is something for everyone to enjoy in this anime. There's also some romance, but it's slow developing, and not super prominent, it becomes a lot more prominent in season 2. I'm also reading the manga, and right now, some very big development is going on in that department. Just try the show, even if it doesn't seem like your thing.