There are 2 popular gyms

–Mankong Phranai Muay Thai Gym

Budget: 500 baht per person
Address in Thai: ยิมมวยไทย สาธร 1
Location: See Map
GPS coordinates: 13.722053, 100.545510
You have some success to contact them through Facebook page Visit

–Muay Thai Plaza 2004

Budget: 500 baht per person
Address in Thai: ซอย แจ๊กเจีย ซอย ศรีบำเพ็ญ
Location: See Map
GPS coordinates: 13.717777, 100.550117