It's really hard to pick a single Ozu favorite. As you may already know nearly all of his films concern the family, ostensibly variations on the same theme of marriage and relationships.
But they're deceptively simple, because nobody does more with less than Ozu, who's almost certainly the gentlest, least pretentious director in history. Even relatively minor works of his like
The Flavor of Green Tea over Rice and
An Inn in Tokyo have much to recommend them. In fact I've yet to see an Ozu movie I didn't like, which can't be said of any other director (not even Kurosawa who I consider the greatest of all filmmakers).
Speaking of whom no arthouse director probably made more accessible and wide-ranging movies than Kurosawa. If you liked
High and Low you'll also enjoy
Drunken Angel and
Stray Dog (if you haven't already).
And for the record
Ran is actually a loose adaptation of
King Lear. Kurosawa did do a
Macbeth film titled
Throne of Blood. Both are first-rate Shakespeare adaptations, especially
Ran which I rate at the very top and in fact agree with the director himself is his best work. (When asked which one of his movies he considered his best Kurosawa would always respond, "My next one." Reportedly that stopped after
Ran.)
But it's a close ball for me between
Ran and
Ikiru. The latter borders on melodrama at times, but it's probably the one Kurosawa movie I'd preserve over all the others, while the former can be easier to admire than to love. Anyway not to be missed in
Ran: Mieko Harada as the vengeful Lady Kaede, arguably the most diabolical villian(ess) in cinema history, and Toru Takemitsu's evocative Mahler-inspired score.
Kuroneko is a horror story, but that's like saying Dreyer's
Vampyr is a vampire movie--neither term doesn't begin to do the movie justice. Like the Dreyer Shindo's
Kuroneko is technically stunning, a 90 minute-long reverie with shimmering haze and atmosphere. And it's strangely seductive when it should be spooky. It's a horror film like no other, and one I hope will gain more traction in the future. See for yourself, and if you like
Kuroneko you'll probably also dig the same director's
Onibaba.
There's nothing I can add about
2001 that hasn't been said. Besides something tells me you're more familiar with it than me.