Many gyms and Rec Centers have a policy that limits access to certain parts of the facility to 16 years and older. Some require minors to be accompanied by an adult or guardian in the weightroom. And some require those between certain ages (usually 12 to 15 years) to take a course taught by a staff member on proper gym etiquette and equipment use before they can use the weightroom (and many still require an adult be present with them).
It definitely depends on the club & their insurance policy. I belong to a gym near my home who allowed my 13 year daughter to join, as long as she was in there with me. I don’t know what age where she’s allowed in there by herself, but I’m not interested in finding out anytime soon! Call the gym directly & they’ll tell you.
It depends not just on the club and the insurance but also on the activity.
One club where I work allows kids age 8 to take cardio classes with a parent in attendance. They can attend independently and have freedom throughout the club when they’re 14. But if they want to do a weight training class, they must be 12. The other gym where I work, it’s 12 in group-ex and 14 for the weight room floor. The place where I pay for membership, it’s full reign of the club at 13.
I am the fitness coordinator at a community rec center. We allow youth ages 13 – 15 to go into our fitness area under the direct supervision of an adult. 16 and up can go by themselves. I also offer a 4 hour Youth Equipment Orientation class for 13 to 15 years olds (and anyone who wants to join in), where we go over every piece of cardio and strength equipment as well as cover some basic principles of fitness (overload/FITT etc.). If they successfully pass the class, we allow them in the fitness area on their own, they just have to wear a bracelet that identifies them as having passed the class.
Most of our adult fitness classes are 16 and up.
Hope that helps!