This mystery seems pretty well solved and closed, but I thought I’d add in a couple extra details for no other reason than to move the “probably” status of Pattison State Park up to “a most likely.” Maybe even an “almost certainly.” 

As noted in Paul’s comment, Google Streetview and satellite imagery seem to show pretty clearly that there is no stone wall where the lake and the river meet. Pattison State Park, however, was constructed by the Civilian Conservation Corps, and a history of that project provides a description of the rock walls that used to be at the exact location suggested:

Another big project was the removal of the bridge abutments and road grade left when the State Highway 35 bridge over the Black River was moved in 1932. Concrete abutments were demolished, the old grade was leveled, and landscaping and tree planting done. In addition, the river banks both below and above the bridge were protected from erosion by rock walls. Stones weighing as much as 600 pounds were hand maneuvered into place.
The photo also shows vertical barriers around the swimming area that don’t seem to be a part of the beach area of the state park. But they can be seen clearly in a photo dating from the construction of the beach (from the same CCC history) and in an old postcard of the beach. 

While that doesn’t conclusively prove that it is Pattison State Park, it seems to remove any reason to believe that it isn’t, particularly in the context of Locklear’s family history there.