I don't live in Houston but I get there frequently for business and may be able to offer some suggestions. First, it would helpful to know what area of Houston you'll be in during your stay. Houston is the 4th largest city in the country with a land mass of around 600 square miles. By comparison, Chicago, the 3rd largest, has a land mass of around 225 square miles. Also, it would be helpful to know what day of the week you'll be there as many of the types of places you're looking for are only open a few days a week.
When most folks refer to "Authentic Texas BBQ" their generally referring to the BBQ found in central Texas in towns such as
Lockhart, Luling, etc. The BBQ traditions in that part of the State are an offshoot of the Germans who immigrated there in the late 1800s. Houston, in the Southeastern part of the State, developed from totally different demographic roots. The BBQ in Houston is more along the lines of traditional Southern BBQ rather than the BBQ found in the central part of the State.
As far as recommendations are concerned, first, avoid Goode Company BBQ and Pappas BBQ. They both fit the description of the type of place you said you didn't want to go to.
A short list of some places that I think might fit your criteria, the items that I've had and enjoyed, and the general location relative to downtown Houston,are as follows:
- Gatlin's - Ribs
- Pierson's & Co. - Pork butt
- Burns BBQ - Ribs
- Virgies - Brisket
All the above are located in various parts of Northwest Houston. Another spot, in Southwest Houston, known as Luling City Market, does a pretty decent job replicating the BBQ of central Texas, but my experience there with brisket has been hit or miss. Also, it's not a mom and mom place and is located adjacent to an upscale shopping mall, The Galleria.
Enjoy your trip.