I spend an unhealthy amount of time sitting around and watching weird Japanese films. Especially New Wave and art works.
These are some of my favorites:
All About Lily Chou-Chou, Nanami:First Inferno of Love, Gemini, The Emperors Naked Army Marches On, Electric Dragon 80,000 volts, Pastoral:To Die in the Country, Snake of June,Dead or Alive, Moonlight Whispers, Kanto Wanderer and of course, Akira.
Legato: Good drama with a story is pretty much everywhere in cinema. Jovial_Jon was on point to suggest the fantastic All About Lily Chou-Chou however there is a decent amount of violence but it is not sadistic like Blue Spring or Battle Royale. I think you should actually look into a Korean film called Spring, Summer, Fall, Winter...and Spring. It is a beautiful piece that meditates on the nature of violence without actually showing it. The director is one of my favorites and also did The Isle (Seom) which was slightly more popular.