Cinematheque KOFA at the Korean Film Archive screens films ranging from Korean classics to Korean and foreign arthouse and independent films for free. Most screenings are open to public but the special and featured programs are aplenty too. Make your reservations on their website or get tickets on-site.
Doosan Art Center runs the Doosan Humanities Theater from March till June. The theater features a series of film screenings, guest lectures on social sciences and humanities, performances, and exhibitions. This year's theme is "exception," and three relevant films will be screened on June 1st, 22nd, and 28th respectively. A Q&A with the director follows each screening. Reservations can be made online.
Myeongdong Art Theater, usually used for theater productions, is now showing films as well. With the seating arrangements as they are, watching a movie feels like a night out at a classic theater. The films are usually remakes of the play being staged that month. However, screenings are irregular, so be sure to check their website for more information. Reservations are made online.