Well, a few factors to consider before heading to central Seoul for a quick visit. Most recent visit to Seoul for me was last Fri and Sat so quite fresh experiences.

1) Traffic is heavy from dawn until dusk and then again. As said before on these boards no probs until GMP airport which the road from Incheon bypasses on the way to the city but after that it can be nightmarish at worst. No rail connection between ICN and the city so best bet is a Limousine Bus.

2) Travelling by subway is efficient if you check routes etc. in advance over the net. But be prepared for full carriages and queing for the trains. Now, this feels very different after an intercontinental flight compared to taking the subway at home. Subway stations have signs in Korean and English so maneuvering there will not be a problem.

3) The majority of people in Seoul speak only their native Korean and you will not be able to understand most signboards and shop & restaurant names as they are written in Korean alfabet. Also in most restaurants menus are only in Korean and staff will not speak or understand English.

4) The physical distance between the historical sites North of the Han River and the main Shopping and Entertainment districts South ( apart from Itaewon ) is quite considerable so if you want both plan well ahead.

5) The Hyatt at ICN offers a nice Spa and dining. You also have the opportunity to play a round of Golf in the immediate vicinity of the Airport if you book ahead.

I'd go for ICN and experience more scenic parts of Korea with more time in my hands at another occasion.

EDIT: The Hyatt offers the best amenities by far.