South Korea is a relatively small country and domestic travel is both cheap and convenient. With more young Koreans spurning the traditional package tour complete with transporation, hotels, and guide, hostels have become more and more common in Korea over the past decade.
Jeju is the premier vacation spot in Korea and there are several youth hostels on the island. However, most of the hostels do not have English websites or English speakers to answer phone calls. Here is one:
Here are some good links for information about traveling around South Korea:
Some websites for info about Korea tours in English:
There are three airlines in Korea: