An online acquaintance lives in Houston and I'll bounce your question off of him. In the meantime, in BBQ USA Steven mentions Thelma's Bar-B-Que on Live Oak Street but keep in mind the book's almost 10 years old.
"Sure! My all time favorite is Houston BBQ company at Eldridge parkway and Enclave. It is on the west side of Houston in the energy corridor. They have a sauce like no other and is worth the drive. Also need to try their home made sausage - especially jalapeño.
There is gas station chain in TX called Rudy's and there should be one near wherever they are. The food is awesome! They have a lean brisket that is great and a nice spicy sauce. They also have what they call their sissy sauce. Going here you definitely want to try the green chile stew and cream corn.
Demeris BBQ is more centrally located at 290 and 610- very traditional and I have never had anything bad there.
Spring Creek BBQ is a Dallas chain that recently moved down here. Not my favorite (sauce) but a lot of people seem to like it. Definitely not Houston style though (they use plates!)
Big Daddy's BBQ is the chain Spring Creek tried to buy but wouldn't sell. Not as good as Houston BBQ co but better than spring creek in my opinion.
There is Pappas BBQ that I have never had but a lot if people like.
They definitely need to check out Pappasitos (Mexican- best fajitas ) and Pappadeaux (Cajun -try bacon wrapped jalepeno shrimp). Both are locally owned by the Pappas family that own Pappas BBQ.
Another good Mexican place is Chuys- was a local Austin place that has expanded. I would suggest the downtown location on Westheimer. I get the southwest special or Elvis platter