The nearest airport is in Seoul (ICN-Incheon Intl.), located 21.7 mi (35 km) from the city centre. If you can't find a flight that works for your travel itinerary, you could book a flight to Seoul (GMP-Gimpo Intl.), which is 1.1 mi (1.8 km) away.
Catch a ride on the metro at Sinbanghwa Station for ease of access to the rest of the city.