Western classical music has much the same powerful place to fill in Japan as it does in middle class America. I'm more aware of it now than usual perhaps, as I have one child studying recorder, and the other taking violin lessons. Two exceptional works from the world of anime revolve around this music.
Nodame Cantabile, one of the hits of the Japanese manga world, just completed an eight year run (reprinted in 22 book length volumes) that as spawned live action and anime movie trilogies (the last two parts of the live action movie are due to be released next year) and a worldwide following. It features a sloppy, expressive piano student, Nodame, and her perfectionist next door neighbor, fellow music student and not easily won boyfriend, who aspires to be a conductor.
The light drama is quirky. Its rich characters, some of whom (including Nodame) are based on real people with the same names, have rich relationships that often go in unexpected directions. Minor characters include a brilliant but perverted European conductor teaching at their Japanese school, a gay timpani player with a crush on the male protagonist, and an electric violin playing buddy of just about everyone in the story.
My beloved wife on trips to the local library complains to me sometimes that everything new in print that is either based on somebody getting killed, or is hyper-formulaic women's fiction where a protagonist is a florist, coffee shop owner or caterer, and/or someone is literally using magical powers to win over lovers. Nodame Cantabile is an exception to this rule, it is not violent without being predictable or impossible.
For younger audiences there is the sweet, short anime series Piano, in which a middle school aged girl, Miu Nomura, who is a long time piano student, tries to figure out her life in the face of ambivalence about how serious she is about her music, while her older sister has left home, her parents are struggling in their marriage, and her best friend seems to have such clear direction in her life about sports, boys and all of the other awkward elements involved in coming of age. While it may be coincidence, it was not long after my kids and I watched this that they got the instrument bug, and they did really enjoy it. The Denver Public Library has at least one set of the series.
Both rise above the sometimes hollow girlish or boyish stories that dominate run of the manga series and are easily accessible to people who aren't hard core manga or anime fans.