Question:
Is it halachically permissible to build a gym – cardio and weightlifting – in the bottom of a synagogue?
Answer:
It is permitted, since there are only prohibitions with building on top of a shul, or having a bathroom under the shul. It is preferable that the entrance to the gym should not be the same entrance as the synagogue, especially if people coming and going o the gym will not be dressed properly.