Not 100% sure, but I believe Club Nautic has a public gym (at the Cambrils end of the promenade). Many hotels also have gyms now, and you can usually go in and use it FOC, although as I said, I am not sure.
I will see if I can find out...I know there used to be a gym down by the railway tracks /station in old Salou, but again, not sure if it is still there.
There is a public Gym in the sports / swimming center on Carrer de Mila in the old town. €4 a day you need to take your passport along and also some change for the lockers.