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A major religion in Korea for a long time has been Buddhism. Even if Joseon Dynasty (founded in 14 Century) officially chose Confucianism as a national belief, Buddhism was still respected nationwide. Therefore, every location where we can find temples has perfect fengshei in Korea. Those places have amazing and picturesque scenery in Korea. Anytime is good to visit, but in autumn with fiery leaves would be better.
If you visit Korean temples in country side on lunch time, they offer the vegetarian temple-style lunch. Korea is not easy for vegetarians to find right restaurants but you can find best vegetarian meals in Buddhist places.
Personally, I recommend hiking to visit these temples. It would be unforgettable hike in your experience. The mountains in Korea aged a lot so quite different from European or American those are steep. The ridges in Korean Mountain are quite attractive. At the end of those ridges, you will find wonderful temples.