The temples of South Korea are always one of my favorite things to check out while traveling there. For one, the temples in South Korea are usually accessible by hike and are often perched on the top of a mountain so just getting to the temple can often be a very fun adventure. The temples are almost always ornate and many date back hundreds of years. Most temples cost nothing to enter and are open to the public.
If you happen to be in South Korea on or near Buddha's Birthday, then the temple experience will be enhanced by thousands of "wish lanterns" that light up at night! This is a breathtaking experience! And with most celebrations in South Korea there is always good food involved!
Buddha's Birthday is a floating holiday based on the Chinese Lunar Calendar so nailing down the date might be a challenge. Celebrations and festivals happen on the weeks leading up to the date as well including the Lotus Lantern Festivals, so you have a a descent window of time to catch the temples decorated in lanterns for the event, but their illumination seems to be limited to the birthday celebration itself.
All I can say is there is nothing like seeing a Buddhist temple ordained with thousands and thousands of colorful lanterns lit up at night... nothing!