To be honest....none of the beaches in/near town are swim worthy. Sewage, garbage, nastiness of third world proportions. I lived there in 1999 and things have really changed since the Canal was turned over to the Panamanians. Many parts of the old city were being redone so maybe the beaches have been cleaned up a bit. The ones right in town are rocky anyway. There is a beach out near the old Howard AirForce base that was OK if you need something close to get your beach fix, however the sand fleas were horrible when I was there.
The best things about "outdoor" Panama require a bit of travel, though all are worth it. Depending on how much time you have you can either charter a boat and go out to Taboga or Contadora, fly a metroliner over to Bocas del Toro which is great, drive up to the Caribbean town of Portobello. It's an old Spanish fort. From there you can take a water taxi out to Isla Grande I believe it's called. I learned to scuba near there. Many Panama City locals used to go to San Carlos which is west of the city on the Pacific. Think there is some surfing and stuff there and the beach is supposed to be quite nice. The nightlife in town is not to miss....esp if you are single. I miss the place. Take me!!!