The nearest airport is in Seoul (ICN-Incheon Intl.), located 30.3 mi (48.8 km) from the city centre. If you're unable to find a flight that fits your schedule, you could book a flight to Seoul (GMP-Gimpo Intl.), which is 10.5 mi (16.9 km) away.
Catch a ride on the metro at Itaewon Station for ease of access to the rest of the city.