In addition to the ubiquitous number of Korean-style drinking restaurants, there is a small strip with a few western style bars and Korean style clubs. The strip is located on the way from the main circle to the harbor in Seogwipo. On the way down the hill the strip will be located on your left hand side.
Milano
Great views, cheap booze and good food. Smoked chicked to share 2-4people, 17,000won. Highly recommended. Sign is only in Korean, but it is the bar on the way down the hill towards Cheonjiyeon Falls in downtown Seogwipo. Look for the bar with a log-cabin feel.
Red Marin
Across the water from Milano in downtown Seogwipo, towards the harbor, is a small waterfront bar called Red Marin. The exterior of the bar looks like an old ship, complete with lights hung over an old mast. Inside, a small store serves as the restaurant, where you can choose from a large selection of Korean alcohols. Grab a table by the water if you can, and enjoy the view.
Gecko's Terrace
A fairly new entry in the Gecko's Terrace franchise of full-sized proper Western-styled bars and restaurants and the only true expat establishment on the island. The bar has a handful of real beers on tap including Guinness as well as a Western food menu including real, unfrozen steaks and a couple of vegetarian options. Open for lunch as well as in the evening. Prices unfortunately are at Western levels think 10,000-30,000 won a meal.