I went here before, but they recently moved to TimeSquare! It's so much bigger, and the location is great! Easy transportation, and since it's inside a mall, you can go there while visiting Timesquare.
Also, this hasn't updated the new location: 서울 영등포구 영중로 15 타임스퀘어 지하 2층
Inside, there is a Dokdo model (as shown in my photo)
There is a lot of info about Dokdo, learned so much going here. It's a great museum for tourists and for learning more about Dokdo.
If you have kids, I recommend going here together since there are a lot of activities to do!