If you go to PINS, there is a pedestrian-only beach called Malaquite just a few miles after the entrance. You can park and walk down quite a ways. I like it there because there are no cars and on the weekdays, not a whole lot of people, although school is out now....

You could also rent a kayak in Port A and kayak around Redfish Bay or Lighthouse Lakes, always cool stuff to see and it's not very expensive...