the nearest one to you would probably be Patong. I would rather go with a gym that knows what they're doing and has experience handling the visa to not complicate things.
I've also been looking in Phuket and there are options in Rawai, Karon, Kathu and Patong. They're sprinkled in various comments so I think first it's important to know where you're located as you probably want to go with the place that is closest to you