Where the Rio Grande spills into the Gulf of Mexico, there's a cruelly gorgeous state park with miles of untouched shores. Boca Chica has tidal flats dotted with shorebirds and lomas, clay mounds covered in brush that rise above the water, which are habitats of the endangered ocelot. There are gorgeous drives all around the area, but the arguable winner is the beach itself with its warm Laguna Madre waters. This beach is a no-frills one, so go before you go and pack everything that you'll need. And as camping isn't allowed, Brownsville is the best nearby option for room and board.
In the small town of Freeport slightly south of Galveston, this maintained beauty of a beach is a perfect escape from the crowds of its coastal neighbor. Stay in the nearby Ocean Village Hotel right on the water, where there's a comfortable bustle of activity minus the tourism and customary trash of the more crowded Texas beaches. Make a trip out to the gorgeous Surfside Jetty Park if you've had too much swimming to look for some dolphins and people-watch.