The nearest airport is in Seoul (ICN-Incheon Intl.), located 23.6 mi (38 km) from the city centre. If you can't find a flight that's convenient for your trip, you could book a flight to Seoul (GMP-Gimpo Intl.), which is 3.1 mi (5 km) away.
Catch a ride on the metro at Jeungmi Station for ease of access to the rest of the city.