Not sure what you are all looking for, I spent a short weekend down at
Palmetto State Park I took my lacy with me and a buddy took his German Shepard mix. For a 2 day trip it was a nice little camp.
I can't remember any of the State parks where I haven't been able to bring my dog. If you like rock climbing then Enchanted rock is pretty fun.
Colorado Bend is also a pretty cool State park, not sure on dogs.
If time isn't an issue I recommend Big Bend federal park. Part of the primitive camping is only accessible by 4x4. Last time I was out there I saw a Mountain Lion and a Black Bear. BAH just pulled this up and it says that pets are not allowed on the trails.
Texas Parks and Wildlife Department:Find a Park
TPWD has only this requirement about pets.
Pets not allowed on State parks
A domesticated companion animal accompanying a person who enters or uses a state park. In no event shall a pet under this subchapter include the following:
(A) a dangerous wild animal, as defined in Health and Safety Code, §822.101;
(B) wildlife;
(C) livestock and exotic livestock as defined in Agriculture Code, §§1.003, 142.001, and 161.001;
(D) any species of animal that is not ordinarily domesticated; or
(E) any species of animal that a person may not legally possess.
Pet Requirements
Pets. It is an offense for any person to:
(A) bring into, possess, or permit to roam within a state park a pet, unless the pet is secured by a leash not exceeding six feet in length, confined in a vehicle, or confined in a suitable cage;
(B) bring into or possess within a state park an unattended pet;
(C) fail to immediately collect and properly dispose of fecal material deposited by a pet for which a person is responsible. For purposes of this paragraph, “properly dispose†means to deposit fecal material in an appropriate solid waste collection container;
(D) bring a pet into an area where pets are prohibited;
(E) permit a pet (except a trained assistance animal accompanying a person with a disability) to enter into or remain in any building or enclosure designated for public use including, but not limited to, a restaurant, snack bar, cabin, lodge room, restroom, park store, shelter, refectory building, amphitheater, administration building, or railroad coach;
(F) permit a pet in the water of a designated swimming area or to permit a pet animal (except a trained assistance animal accompanying a person with a disability) within the land or beach area adjacent to the water of a designated swimming area; or
(G) possess a noisy, vicious, or dangerous pet, or a pet which creates a disturbance to or hazard within a state park;