Gyeongju National Park wraps many of the city's mountain sights into a wider protected landscape of forest trails, temple routes, and Silla-era remains. It is less a single gate-and-ticket attraction than a set of hiking areas around Gyeongju, with routes leading up into the hills above the historic city.
Take a map before setting out, since English signs thin out once you are away from the main approaches. The park is especially useful if you want to balance Gyeongju's tombs and museums with a day on foot.