The only major temple in the middle of Seoul, Jogyesa is at the center of Seon (Zen) Buddhism in Korea. Although the temple itself was founded in 1910, some of the trees in front of the main building date back almost 500 years. The main building, called the Daeungjeon, was constructed in 1938 and still retains its brilliant colors. Not the most stately or the most beautiful temple in South Korea, Jogyesa's main strength is its convenient location.
Although not a place for quiet contemplation (you'll be hard-pressed to find a busier temple in the country), it's still worth stopping in, as the temple offers a variety of programs that teach visitors about Buddhist life (tickets are W10,000). They require that at least six people be signed up to participate in each program, so you'll need to make a reservation at least a week in advance. English interpreters are available.
Around the temple, there are many shops that specialize in Buddhist items, such as prayer beads, wooden gongs, and incense. It's worth a browse in the stores -- perhaps a small Buddha will make his way into your luggage.