Do you know what area you want to stay in Seoul? Banana Backpackers seems to be very close to Insadong area. I have stayed at Hotel Sarangbang, which is literally in the Insadong area. I assure you it is no longer a Sarangbang (love room). Check other visitor's review on hotels.com. I've also had some friends stay in Hongdae area at An Nyoung Guesthouse.
Website here. You can read reviews
here. They really enjoyed being in the area, and the owner was very helpful and friendly. Even ordering McDs delivery as it is not something they have in the States (the delivery, not McD).