Names in this area must have been hard to come by, because authorities decided to confuse everybody by christening a bay, a town, a county, a peninsula and an island with the same name – Matagorda. The tiny town, little more than a handful of stores and homes, offers a link to the peninsula (Matagorda Peninsula, not to be confused with Matagorda Island, the remote state park off Port O'Connor), a popular spot for fishing.
There are 23 miles of lonely white-sand beaches out here. In Matagorda buy a $10 permit at Stanley's Market or CJ's One Stop, and then drive out onto the beach and stake your claim. Note that the beach is legally a state highway with a speed limit of 20mph, and all laws still apply. If you're not in a 4x4, you'll do better to hike in.