The Kenworthy Performing Arts Centre at 508 S. Main is a former movie theater which has been refitted with a stage for live performances. The Kenworthy family donated it to a community foundation which runs it as a nonprofit venue for some of the coolest entertainment in town. Besides live theater and musical events, it also shows second-run, independent, classic, and foreign films (the latter concentrated on Sunday nights in its Film Society series). Tickets are incredibly cheap: $4 (half that or less if you buy a Film Society season pass).
The theater is being lovingly restored. Note the 1920s marble switchboard behind the concession stand.
One of my favorite features is the way selected seats have been removed. Choose your place carefully and you can stretch your legs out. The spaces also minimize the danger of tripping over other patrons as you make your way to the lobby in the dark.
Kenworthy Web site
Another place to see unusual films inexpensively is the University of Idaho's Student Union Cinema Series.
The SUB films page