I've searched a few threads related to the topic, but none quite answer my dilemma - I will be arriving in ICN at 6pm and flying out the next morning at 9am ... should I take the train into Seoul for the night or stay closer to the airport?

I realize near the airport would be cheaper and easier, but is it worthwhile to go into the city? At best I will only have a few hours - after security and the train in, I figure I'd get there around 9pm and then would want to leave around 6 am or so.

Thoughts?