I just showed this for one of our movie nights! Tarkovsky is one of the great Soviet directors. Long shots, lots of water, beautifully composed. Solaris (1971?) and Andrei Rublev (1966) are great if you're looking for more by him.

Stalker was filmed in and around Tallinn, IIRC. The shoot was downstream of a chemical plant and an abandoned hydroelectric plant. As for how they got (access to?) those locations, Soviet filmmakers could do all kinds of stuff one couldn't in the studio system. There's some interviews with Tarkovsky about the creative process there.

They actually shot the film once, but it got developed incorrectly, so they had to shoot the entire film from scratch.