Photo: Wikimedia Commons (CC BY-SA)
한국은행 화폐박물관
Museum · Jung-gu
The 1912 Renaissance-style former bank building, a listed heritage site, is a sight in itself. Easiest to reach by subway.
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Source: bok.or.kr
Postage Stamp Museum
FreeMuseum · Euljiro 1-ga Stn. (Line 2) Exit 6, Myeongdong Stn. (Line 4) Exit 5
A compact free museum on the history of stamps. In the middle of Myeong-dong, so it's a handy escape from the heat or cold.

Woori Bank Museum of Banking History
FreeMuseum · Hoehyeon Stn. (Line 4)
A small free museum in the basement of Woori Bank's head office. Open weekdays only, so a lunchtime visit works best.
Seoul Plaza
FreePlaza · City Hall Stn. (Lines 1, 2)
The lawn plaza in front of City Hall, host to many festivals and events, plus a winter ice rink. Little shade, so pair it with a walk along the Deoksugung stone wall road.
Sungnyemun Gate (Namdaemun)
FreeHistoric site · Hoehyeon Stn. (Line 4)
National Treasure No. 1 and the south gate of the Seoul City Wall. Open free of charge up onto the wall, with a changing of the guard ceremony on weekdays.
Jeongdong Observatory
FreeViewpoint · City Hall Stn. (Lines 1, 2)
A free observatory on the 13th floor of the Seosomun Government Building. Sweeping views of Deoksugung Palace, Jeongdong-gil and the City Hall area, with Cafe Darak for a rest.

Seoul Metropolitan Library
FreeLibrary · City Hall Stn. (Lines 1, 2)
A landmark right in front of Seoul Plaza. Known for its stepped bookshelves and glass-walled plaza views, with a rooftop and cafe for a break.
National Museum of Korea
Partly freeYongsan-gu · Ichon Stn. (Line 4, Gyeongui-Jungang Line)
Korea's largest museum, with all permanent galleries free. The spacious lobby and Reflecting Pond garden are good for a rest, and Wednesday and Saturday evening openings are quieter.
National Folk Museum of Korea
FreeJongno-gu · Gyeongbokgung Stn. / Anguk Stn. (Line 3)
A free museum of Korean daily life. The outdoor Memory Street and children's museum make it great for families.
Seoul Museum of History
FreeJongno-gu · Gwanghwamun Stn. / Seodaemun Stn. (Line 5)
A free museum on Seoul's transformation from the Joseon era to the present. The old Tram No. 381 outside is a photo favourite.
National Museum of Korean Contemporary History
FreeJongno-gu · Gwanghwamun Stn. (Line 5) Exit 2
A free modern history museum facing Gwanghwamun Square. Insider tip: the rooftop viewpoint takes in Gyeongbokgung and the square at a glance.

Korean Film Museum
FreeMapo-gu · Digital Media City Stn. (Line 6, Airport Railroad, Gyeongui-Jungang Line)
Free museum covering 100 years of Korean cinema. The on-site film archive library screens classics at no charge.