The National Museum of Korea is a wonderful tourist destination in Seoul. I recommend it very highly.
The modern museum (built in 2005) is very spacious and filled with wonderful works of art. It provides a sense of the long history of Korea. It is very well laid out and includes enough information on the works to give you a sense of the context.
The museum displays relics and artifacts in six permanent exhibition galleries: Prehistory and Ancient History, Medieval and Early Modern History, Calligraphy and Painting, Asian Art, Sculpture and Crafts as well as one gallery highlighting donations.