Gyeongui Line Forest Park is a lovely place to take a break. Have a picnic, kick a ball around or just lie on the grass and close your eyes for a while.
You'll soon find out why this Hongdae recreation and green space is visited by many travelers. If you're looking for more to see and do here, Gyeongbokgung Palace, Dongdaemun History and Culture Park, and National Museum of Korea are in the area as well. They won't take you very long to get to from Gyeongui Line Forest Park.