An update: I managed to find the Sky Club in Ahyeon elementary school. The entrance is a bit tricky especially since it gets dark pretty early in Seoul these days. I printed this picture from oldhand's response and used that to get there. Initially I sent them a message through their website but there was no response so I decided to drop in directly today evening and request for their permission to play. The members were very kind to admit me in and I start playing from this week. They also offered me a nice hot cup of coffee, a piece of chocolate to celebrate Pepero Day and asked me to watch a few games

I could not go last earlier since I forgot to bring my ankle brace and went on a hunt last weekend to find a brace locally. I found the McDavid ankle brace in a sports shop around Dongdaemun stadium. It was quite a hunt, as I went to almost 20 shops around the stadium and came up empty. I was about to give up and go to the train station, when I saw a shop called "Multi Sports Shop" right in front of Exit 4 (I think) of Dongdaemun History & Culture Park station and decided to give it one last try. And I got lucky there! I also saw quite a few shops there selling Yonex, Wilson & Victor racquets - I did not inquire on the prices though.