I have been to many Korean temples, and I never get tired of seeing them. I love the incense smell, the thick wooden floors, the flowergardens and the fact that the buildings are never gigantic, but instead have a perfect shape. Teal is not my favourite colour, though.
So for a nice place to visit I would recommend Naksan Sa (Temple)
in Naksan Provincial Park on the north-east coast, east of Soraksan. There is a very tall statue of the Goddess of Mercy, and gorgeous views of the ocean from a cliffside temple building. If you arrive early it's a perfect place to watch the sunrise, but don't expect to be alone, even mid-week in winter. The main temple has a breathtakingly complex sculpture all of wood.
Even if temples are not your thing, the oceanview is worth seeing.