The nearest airport is in Seoul (ICN-Incheon Intl.), located 24.3 mi (39.1 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 6 mi (9.7 km) away.
Catch a ride on the metro at Guro Station for ease of access to the rest of the city.