I know of one badmiton club in Gohyun. It is a korean badminton club. They normally play every Monday- Friday from 19:30 and later I think. Some days the indoor hall is rented out to other activities. I made a map. It is the indoor hall next to the stadium in Gohyun. There is also two badminton shops on the main road there that sell everything you need and they can re-string rackets etc.
On weekends there is an Indian group that play in the Samsung Rec/Culture centre right outside the SHI main entrance. They play Saturday / Sunday from 10-12 in the morning. I can get you in contact with them.My Korean phone number is:010-3147-7449