If you land at Incheon Airport after normal rail options have ended, do not assume a taxi is the only remaining choice. The airport currently publishes dedicated late-night bus services from both terminals to several Seoul corridors.
The current airport guide lists N6000 toward Gangnam Express Bus Terminal, N6002 toward Cheongnyangni, N6701 toward Dongdaemun Design Plaza and N6703 toward the Gwangnaru area. Intermediate stops include places such as Songjeong, Hongdae, Seoul Station, Euljiro, COEX and Jamsil depending on the route.
The airport currently lists adult fares of KRW 17,000 for N6000/N6002 and KRW 18,000 for N6701/N6703, with a lower fare to Songjeong on the relevant route. Tickets are purchased through airport ticket booths or automated machines, and the airport notes that Tmoney GO is also an option for the N6701/N6703 operator.
Terminal matters: Terminal 1 and Terminal 2 have different boarding areas and departure times. Check the official airport page after landing rather than relying on an old screenshot, because schedules can move with operating conditions. If your hotel is not close to a listed stop, plan the final taxi or local connection from the night-bus corridor.