I personally think Leeum Museum of Art is the best private gallery in Seoul. The gallery building is designed by famous architects such as Jean Nouvel and Mario Botta. This is the perfect place to see the masterpieces of Korean modern art. Their collection includes masterpiecies of most famous Korean artists, Mr. Nam-jun Baik and Jungseop Lee. My personal favorite is Do-ho's Suh's exhibition named 'A perfect home'. Leeum is close to Itaewon and Hyatt Hotel. A must-see in Itaewon and in Seoul.