I recommend staying at a traditional hanok if you ever visit Seoul for an authentic experience. Stay256 was cozy and clean, with friendly staff who spoke perfect English. It's located in the heart of the Bukchon area, with a nearby shuttle that takes you to the closest metro point (otherwise a 15 min walk).
The only downside was that we went during autumn / winter, so the heating was cranked up high. During the day, it was really cozy, but with little air circulation, it got really sweaty and hot in the middle of the night.