[nickels]

I don't know of any in Patong but there are plenty on the island, near Kata Beach, Chalong Bay, etc.



Muay Thai Boxing , Phuket , Thailand - By Muay Thai camp
Phuket Muay Thai Boxing Gym - J.Prapa (good deals, nice beach)
Muay Thai and MMA Training Camp and Fitness Center @ Phuket, Thailand - Thai-Boxing, Muay Boran, Krabi Krabong, BJJ, Submission grappling, Mixed Martial Arts Instruction.

This last one is only for serious fighters:
tigerpitt.com