Originally Posted by
Aventine
Just 24 hour haejang guk and gamjatang places maybe. A lot of the markets don't open until late morning to midday.
Namdaemun has a few rather nice "mandu" dumpling shops that are open early in the morning too. Just walk towards Myeong-dong from the station and stay on the left side of the road.
But really not much else to do that early than for example hiking up to Namsan. The newish park next to the Hilton hotel is a good starting point.