Translation:Where is the gym?
Sports centre is a better translation than gym which has its own word 健身房
That can depend on the word you are saying. The word you found is 健身房, which actually refers to "gym".
When you mentioned "sports center", you are referring to "exercising location", which has the derivative of "exercise". Thus, the best translation is 運動中心.
The preciseness of the translation does not only rely on the translator alone, but the characters that can possibly exist within the origin.
Mine is purely based on everyday language in Beijing over the past 20 years.