I brought my teens with me to the gym on Odyssey. The 17 year old was old enough to go by herself but the 15 year old needed a special wrist band we got from the spa and an adult had to go with him to the gym to supervise
The fitness centers are usually open between 6 and 7 am until evening for anyone, no check in required. There is plenty of equipment and free weights to satisfy them. When you get onboard, look where the center is, let them go visit so they are familiar with the layout and they can plan their routine and verify the hours. It is an early morning ritual for me even at an older age as I still actively engage in competitive sports as there are fewer people up and I enjoy their centers on all the ships we are on.
