There is a Shilla Stay Hotel at Gongdeok station. Prices typically range around $100-150 a night. The hotel itself is new, modern and clean.
Near Seoul Station is 4 Points by Sheraton, Namsan.
Also, there is Courtyard by Marriott in Namdaemun. Brand new and getting good reviews by visitors. Courtyard by Marriott in Seoul are much nicer than ones typically found in the States. You might also consider
Glad Hotel located in Yeoido. Excellent reviews and it would be a nice walk to/from Conrad going through Yeoido park.
I use Hotels.com frequently and the reviews people leave give good insight as to the quality of the hotel. I put some random dates in for Oct. and it was just over $100 a night.
Random tip: Every Friday and Saturday night (6pm - 11pm) until Oct, there are a lot of good food trucks, live music and various items on sale along the Han river at in Yeoido. It is called
Seoul Bamdokkaebi Market.