I recommend Wonju Kyunghee Namu Oriental Medical Clinic.

First of all, it's very accessible, with both underground and above-ground parking. Both the guides and the doctors were friendly and helpful. Their explanations were clear and detailed, so I was able to receive treatment without any discomfort. Also, while acupuncture is naturally painful, some hospitals are particularly uncomfortable, but this one doesn't hurt as much, so I'm even less nervous. I've seen a lot of relief from the pain I've felt since I've been there, so I highly recommend it.