Cheapest
The cheapest place to sleep anywhere in korea is at the local sauna 찜질방 - jimjilbang. this is a kind of bathhouse that has a communal room for sleeping on the floor. it usually costs about 5000-10,000 won. ask a taxi driver for the closest "jimjilbang" or keep an eye out for a symbol that looks like a bowl with steam coming off it.
Motels
Motels abound in korea, and this is no less true in gwangju. the main concentration of motels are in and around sangmu area, between the sangmu and uncheon subway stops and cheomdan area, near the lotte mart. motels can range from 30,000-50,000 and tend to be very seedy. one can judge the quality of a "love" motel by the movie selection usually proudly displayed near the cashier and the vending machines located throughout the motel.
Splurge
There are two quite reputable hotels in gwangju. one is the ramanda in sangmu where a room can generally cost around 100,000 a night. the other, near mount mudeung, is the shinyang park hotel. the sangmu ramanda is more conveniently located for business where as the shinyang park hotel offers a more peaceful and quiet stay.