Seoul's Incheon Airport is routinely voted the best airport in the world. It's probably one of the best airports to be stuck on a long layover. With a Korean culture museum, free cultural shows, and lots of great food, Incheon isn't a bad place at all to have a delayed flight.
Still, sometimes you have a long enough layover that you might want to get out, get some fresh air, stretch your legs, and spend a few hours exploring Korea.
You can purchase a ticket for the 45-minute ride on the Incheon Airport Express from the airport into Seoul in the lower level of the airport. The ticketing area is well-marked and easy to navigate.
Seoul's old royal "northern" palace, built in 1394, is the biggest of Seoul's Five Grand Palaces.
The palace has been destroyed and rebuilt several times throughout its storied history, first by the Japanese in the 16th century, and more recently by the Japanese again during its imperial expansion just before the First World War.
Korea was occupied by Japan until after the Second World War. In the 1980's, the Korean government began rebuilding the royal palace - an effort that was expected to take the next forty years. Now, the palace complex is almost totally restored.
Besides the palace buildings, the complex also houses the National Korean Folk Museum and the National Palace Museum of Korea. Admission to both is free of charge. Both are excellent museums, and well worth visiting.
If you're lucky, you can catch a reenactment of the changing of the guard ceremony. They hold the ceremony every hour on the hour from 10am-3pm. Reenactors dressed like royal guards from the Joseon Dynasty marched in, while the commander of the royal guard watched and directed from the top of one of the huge wall gates.
Yonggungsa Temple was built in 670, but the original buildings were destroyed during Japanese occupation. The new temple was reconstructed on the site and is located on a mountain just twenty minutes away from Seoul's new airport. If you only have a few hours, it's easy enough to get to from Incheon.
The temple is dedicated to the dragon god, and, while small, is a beautiful mountain temple and very atmospheric.
The KR Pass is a train pass offered exclusively to foreigners visiting Korea, and is the most economical way to see the country. Just like Japan's JR Pass, this pass allows the holder unlimited rides on nearly all Korean trains for the valid period, and see as much of the country as you can while saving the most money.