Well Curt, you've already hit on the right country, if not for its best films. Try not only Kurosawa (who needs little publicity) but Takeshi Kitano (violent, humorous cool), Ozu (quiet wisdom), Oshima (radical, challenging) Kore-eda, Imamura, Ichikawa and many others. And not forgetting contemporary animation. Then you can move up to the highest level cinema has yet reached; the films of Kenji Mizoguchi. 

My own 3 strongest recommendations would be; Sansho the Bailiff, Seven Samurai, Tokyo Story, from the 3 most famous Japanese grandmasters.

Of course there are wonderful films in many countries. France has produced a huge number of masterpieces, and i'm also partial to Russian cinema. 