I guess I should have mentioned I will only be in Old San Juan for one day and I will not be wandering that far from the ship.
No beaches very close to the ship. All rocky coastline except a small public beach on the north going toward the Caribe Hilton and another very small beach right over the bridge on Ashford Ave. Never saw any boards, very crowded with locals. Otherwise you have to go our toward the airport Isla Verde area. All beaches are public Except the one at the Caribe Hilton.