Texas has little to no public land, so finding somewhere to go without having to pay is always tricky.. but i found this beach less then 2 hrs from home:
That's the East part of Matagorda (sp?). Take 457 (Sergeant Joe Parks Memorial) south from Sargent, TX and then when you cross the swing bridge over the intercoastal waterway, turn west and drive until you run out of road, then keep going!