Since I started this thread, I guess I should do a summary of the recommendations, so far.
The best non-stereotypical, believable, well-acted movies about Japan are:
Sayonara--won an Oscar or two I believe
The Yakuza
(Black Rain)-- One poster said it's full of cliches
Mr. Baseball-- Mentioned several times (a personal fav)
Bad News Bears Go to Japan
Letters from Iwo Jima
Since there's one WWII movie listed, I'd like to add 2 more:
Bridge on the River Kwai
Hell in the Pacific
Sorry but I've never seen House of Bamboo nor Escapade in Japan so I can't pass judgement. And I have a feeling they are not easily available.
I've heard about Marlon Brando's House of the August Moon in which he plays a Japanese character. Is that any good?