Man with a Movie Camera is my favorite silent film, but Eisenstein's stuff is great, too.

The Cranes are Flying is a top-notch tearjerker.

The Color of Pomegranates is another all-time favorite - stunningly beautiful, more of a poem than a film.

Andrei Rublev isn't recommended as often as later Tarkovsky films but it's my favorite of his. One of the few medieval movies that actually feels medieval (Marketa Lazarova, a Czech film from a few years later, is another).

I've heard great things about July Rain but haven't seen it yet.

Here's a funny Georgian film, Blue Mountains, that's often claimed to be about "the crumbling Soviet system" . . . it's not, it's just a satire of bureaucracy.