That is a little late from the day to have the ability to do Considerably culturally, but you can go into town (I would recommend Hongdae, since it's closest form the airport) and luxuriate in a nice evening meal after which a wander throughout the more energetic area of the town before gonna bed rather early (you'll want to get up all-around 5:30am to have the ability to get within the educate by 6am).
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Even though your luggage just isn't checked as a result of, there is a (paid) spot 분양 in which you can fall baggage, purchasing Each individual hour that you shop them. There is a single in Every single arrivals place with the two terminals. Individually, I might say go with the ten hour layover - for a world flight leaving all-around 9pm, that places you on the metro at five or 6pm, depending on where in the city you go, to get back to the airport before 7pm to go through security and customs again. four will likely be all right, but in some cases you really want five hrs to acquire from the city and to the airport, through security and customs after which you can into the gate on-time.