Seoul actually has 2 airports, if you happen to be going to the one closer to central Seoul (Gimpo) you might be able to do something.
You don’t indicate what time of day you will arrive and depart, but Incheon Airport offers a series of free Transit Tours of varying lengths and departing at various times of the day. The shorter tours are within the city of Incheon, which is a major city in its own right, whereas some of the longer 4- and 5-hour tours are of sights and sites in Seoul.
While such bus tours are by nature superficial, they will give you a small taste of Korea beyond the airport spa. Because no planning effort is involved beyond purchasing the ticket (and because they are accustomed to dealing with rushed travelers), they are far less stressful than trying to tour an unfamiliar city independently in just an hour or two.
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I don’t think you’d have much time- it’s about one hour to downtown by train (they say 43 minutes, but they run 10-20 minutes apart), and of course you’d have to transit customs and immigration both ways, as well as security.
Here is the train schedule.
Credit:stackoverflow.com‘
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