The nearest airport is in Seoul (ICN-Incheon Intl.), located 15.9 mi (25.7 km) from the city centre. If you're unable to find a flight that fits your schedule, you might consider flying into Seoul (GMP-Gimpo Intl.), which is 4.8 mi (7.7 km) away.
Catch a ride on the metro at Jakjeon Station for ease of access to the rest of the city.