The closest airport is Gimpo, about 6000 won by taxi. The issue is that taxi drivers in Korea try to charge you much more, the driver was demanding 20000, basically 3 times over. Same next day when I used taxi to go to Incheon, meter showed 34000, the driver was demanding 50000 won. Shameless! Reception staff will assist you with the reasonable price range, please ask them in advance, before you get in a taxi.