I am already in Downtown in South Korea. Where I can buy the SIM card?
The CUs (CVS) on the arrival floor in the Incheon International Airport sells the SIM cards and so does hundreds of 7-11 in downtown.
If you visit 7-11 in Myong-dong, Dongdamun, Hongdae, Shinchon, Jongno and COEX in Seoul, or 7-11 around Haeundae in Busan, You can buy the 7 days and 15 days Blue SIM.
But, I recommend you not to leave airport without SIM.
It can be a little bit bothersome and hard to find.
You can check where you can buy the SIM through below link.