There are several areas of river access at Pedernales Falls. The impressive floodwater-carved gorge with waterfalls (not visible from the overlook or without a little hiking upriver, and only flowing in periods of non-drought) and several deep pools is along the western edge of the park boundary, marked on the
park map as "Pedernales Falls" and "Cypress Pool".
Access to the river's "beach area" is from a hiking trail near the entrance/ranger station. This area is popular with tubers, swimmers and fishermen.
There's also a travertine and moss-shrouded pool/waterfall named "Twin Falls", but that is closed for revegetation/preservation -- one should not swim or even hike down to that area, but you can look at it from a marked observation point/overlook on the the Wolf Mountain Trail.