I only know about 3 Olympic sized pools. One is in Kiwani's in Clayton, one next to the loteria building in Calidonia (the water is actually better than the building radiates) and the PowerClub in Panama Pacifico.
Kiwani's is $3 for normal people, $2 for people in ciudad de saber and $1.5 for retirees. PanaDeportes in Calidonia is free - no place to relax. PowerClub is $15 but they have no lanes so best to go when no one else is there.