Brad
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The Seoul Museum of Art (free entry) is modern art museum located behind the Deoksugung Palace grounds. Here you can explore several floors which six exhibition halls which feature the works of Korean and international artists works at various times throughout the year.
There is one permanent exhibition "Chun Kyung Ja - Eternal Narcissist, where you can see a handful of works painted by this important Korean artist. During our last visit we found some of the works included in the third floor temporary exhibition - DigiFun Art: Urban Space (22 Sept- 13 Dec 13 2015) quite interesting to see. We also enjoyed the sculpture garden in front of the museum. These are quite photogenic, particularly during autumn foliage time of year.
In the end, the Seoul Museum of Art might be a hit or miss for art fans. There are few exhibition halls and depending on the current exhibitions, there might or might not be much that meets your tastes for art. As such it is best to visit the museum website beforehand prior to deciding to include a visit here or not during your trip to Seoul.