I am flying to Tokyo in November, and I have the choice to go direct (paying extra) or transit via Seoul. Is 6 hours transit time enough to leave Incheon airport for a bit to see something of Seoul? It might make my trip more worthwhile to see something of South Korea too. I don't know much about the busyness of the airport around this time, and travel time between the airport and the city, so that's why I am asking.
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 the 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.
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.
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.