A gymnasium or gym is an area dedicated to fitness and exercise. Some Federation starships were equipped with gymnasiums.
Daniel Radke helped Yh'ahni hone her fighting skills in one of the USS Cantabrian's gymnasiums in 2372. (Star Trek: The Cantabrian Expeditions: "Catalyst, Part Two")
The USS Bajor's officers' gym was on deck 8, and included gravity controls at each station. It also contained a sparring ring. (Bait and Switch: Bait and Switch, The Wrong Reflection)