Gyeongju is a very cute little city, south east from Seoul. It's the ideal place for cultural tourism as there are many ancient relics, tombs, palaces, museums and temples. It has been the religious centre of Korea and the old capital of the Sylla Kingdom (57 BC-935 AD) and has several UNESCO World Cultural Heritage sites. It is a famous touristic city for locals, yet you won't see that many westerners and be able to feel the authentic spirit of a korean city. Easy to reach, the National Park nearby offers several scenic trails and the Bulguk-Sa Temple is one of the most impressive temple in this country. It's a city not to miss while in Korea !
One tip : visit the town riding a bicycle ;)