Gyeongju was the capital of the Silla kingdom for almost a thousand years, and the whole city still feels like an open-air museum with the labels politely removed. We visited in May 2021 and did the best thing you can do here: waited for dark and went walking.
Gyeongju rewards an overnight stay: the tour buses leave, the lights come on, and twelve centuries of history get very quiet and very photogenic. It is an easy trip up from Busan.