Hugging the border just above where the Rio Grande empties into the gulf, Boca Chica is a rarely visited 10,680-acre wilderness very literally at the end of the road. SpaceX's proposed launch site nearby may change all that, and will certainly have some impact on access, but for now it's a peaceful slice of sand dunes away from the world.
The area is administered by the US Fish and Wildlife Service's Lower Rio Grande Valley National Wildlife Refuge. Facilities are non-existent, so take everything you'll need, but be aware that camping is not permitted.