There is a nice quiet Gym at Ege saray Marina Hotel in fethiye, aircon and overlooking the Marina. Can get you details re price etc if you inbox me, they also have a beauty salon, Turk Bath etc,
There is also a Gym above or near Esnaf Hospital Fethiye, a friend uses and says its good, the one near Tansas is cheap but I dont like the look of it myself because its open, so everyone can see in from the main Road