The reason I ask is that I've never been to Seoul.

I debated about staying in the city overnight, but with a 5:45pm arrival and a 1:10pm departure the next day I don't think it is worth it.

I figure the earliest I would be at a hotel would be 8pm and I would have to leave by 9:30am the next morning.

I think in this case I'll just have to settle for staying at the airport at the Hyatt.