Hard to believe but you can check-in for both Incheon and Gimpo in Gangnam. There is a City Airport Terminal in the Korean World Trade Center .
For more information about the check-in process follow the above link to the city airport terminal.
You can take the subway to Samsung station (Green Line, line No.2) and walk to the KWTC exit. Or you take the Bus and get off at the bus stop in front of the Grand Inter-continental Hotel.
It is also possible to return a rented mobile phone of KTF and SK Telecom.