There are many boxing gyms in Fort Lauderdale area. However, most of them do charge for one on one time with a trainer. You might try contacting the following gyms:
1. Revolution Fitness Training
http://www.revfittraining.com/2. RFLX Training Center
http://rflxtrainingcenter.com/3. Hammer KickBoxing
http://hammerkickboxing.com/Most gyms charge for the time due to the demand for the space. You might be able to find a window of time that is not as popular for which they might be willing to either give a discount or use the space.
Hope this information was helpful!
