Decent Cheap Hostel in Seoul near busline to Incheon Airport

Hello

I was hoping to find a decent cheap hostel to get some sleep in when I arrive in Incheon. I have a lay over getting in at 5:30 pm and my flight doesn%26#39;t leave until 3:30 the next day. I wanted to go to Seoul and walk around a bit, get some food and sleep, wake up and see a little bit before getting back on the bus to catch my flight. Anyone have any suggestions?

Also any suggestions of interesting and inexpensive things to do? not really interested in shopping.