The Hanok restaurant Yoomi opened is called Permil.
韓文名稱 Name in Korean：퍼밀
地址 Address：서울 마포구 동교로46길 26 1층
The alley they have walked past on the way there is also just close by, it can be found by this cafe (which is the one I have marked by the blue circle on the screencap above).
韓文名稱 Name in Korean：타나리헤나카페
地址 Address：서울 마포구 성미산로 200