A meigaza is an old-style repertory cinema that shows films after their first run, usually two back to back for a single ticket, with programs built around a director or an era. Pick a double bill from the schedule and settle in among local film fans. Japanese films are usually shown without English subtitles, so choose a foreign film in its original language or a screening marked with English subtitles.
A neighborhood repertory cinema near Takadanobaba Station in Tokyo that changes its double bill every week, so one ticket covers two films. Tickets are sold at the box office on the day only, and it is cash only. Its English page marks the films that have English subtitles.
A large repertory cinema a few minutes' walk from the east exit of Ikebukuro Station, known for director retrospectives, screenings on film and all-night programs of several films in a row. Tickets are sold online as well as at the counter, and cards are accepted. English subtitles are rare, so check each screening before you go.
A single-screen repertory cinema right under Minatogawa Park in Shinkaichi, an old entertainment district of Kobe. It shows double bills of films after their first run, plus early-morning and late-night screenings. Kobe is about 30 minutes from Osaka by train, and foreign films come with Japanese subtitles, so pick one in a language you understand.
A small repertory cinema in the Maruyamacho area of Shibuya that runs long retrospectives built around a director, a studio or an era, of old Japanese films and Hollywood classics. Japanese films are usually shown without English subtitles. A program of foreign classics in their original language is the easiest choice.