Looking at Daum map, looks like Euljiro 3-ga Station will be nearest to Supyo Bridge. The station in south of Cheonggyecheon stream, about 5mins walk. i'm guessing your guesthouse is near Hyehwa Station on line 4? Take line 2 to Hyehwa Station, with one transfer at Dongdaemun History & Culture Park Station (to line 4).
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