The city of Gyeongju was one of the most important cultural centres that I visited during my stay in Korea, with a large number of interesting sites and relics. Among them, the Seokguram Grotto is an artificial cave dating back to the 8th century that was built on the side of a mountain at the same time as the nearby Bulguksa temple. The statues of Buddha situated inside are very impressive. If you can, watch the sunrise from the cave, as the view is particularly beautiful.
Close to the national museum, I found that Anapji Park was worth a visit, especially in the evening, when all the buildings (fully restored and rebuilt) are lit up and are reflected in the artificial lake.
Don't forget to try out sambap, the culinary specialty of the city, during your visit to Gyeongju. It consists of rice and seasoned meat wrapped in lettuce and accompanied with a sauce.