GETTING THERE: There are no direct flights to Cheju Island from the United States. United Airlines offers daily flights from Washington to Seoul; the airline currently is quoting a round-trip, midweek fare of $1,099, with seven-day advance purchase required. In Seoul, you can connect with a Korean Air flight to Cheju. Flights leave Kimpo Airport about every two hours; the round-trip fare for the one-hour flight is less than $100. Flights also leave from other Korean cities and from Tokyo, or you can reach the island by ferry from the port city Pusan. WHEN TO GO: The weather on Cheju Island is fairly mild most of the year. Winter winds can be very cold, but the southern side of the island is noticeably warmer because it is shielded by Mount Halla. Summer is mild and comfortable; spring and fall are cool and pleasant. Most outdoor sports can be enjoyed throughout the year, though the water is too cold for swimming from mid-fall to late spring. GETTING AROUND: Tours can be arranged through hotels or the Cheju Travel Service for about $35 per person for two days. Taxis can be chartered all day for $40 to $50 (set the fare before taking a tour). Buses cross the island at 15-minute intervals from Cheju City to the southern coast village, Sogwip'o. The ride takes about 1 1/2 hours and costs about $1.50. Another bus follows the coastal highway around the island. The cost is about $2.50, and the trip takes about six hours. Hotels provide schedules. WHERE TO STAY: Cheju offers a wide variety of places to stay, with hotel rates ranging from about $20 per night to more than $100. For traditional Korean overnight accommodations, stay in a yogwan. There are many of these small inns around the island. Rates range from $10 to $15 per night for two, but you'll have to sleep on the floor (which is heated on cool nights). A mat and blanket are provided. Some of these inns serve Korean food, and have bath houses nearby. Reservations are rarely needed. WHERE TO EAT: The Western-style hotels offer international meals. For a taste of the spicy traditional Korean foods, stop in at any of the many small restaurants scattered around the island. A popular meal with Americans is bulgogi, a barbecued meat. The spicy, fermented cabbage dish kimchi comes with every meal. Korean meals are inexpensive and enjoyable, and $5 can cover a table with a variety of interesting dishes. SHOPPING: Small lava-rock carvings of the tolharubang are popular items in the island's souvenir shops. There are also antique shops that offer Korean artifacts at good prices. In Hallim, a village on the west coast, an Irish Catholic mission produces woolen clothing in traditional Irish patterns. Visitors can see flocks of sheep grazing on hilly green fields, and can visit the factory where wool is turned into clothing. INFORMATION: Contact the Korea National Tourism Corp., 460 Park Ave., Suite 400, New York, N.Y. 10022, (212) 688-7543. -- Fariss Samarrai