My impression is that Houston is a bit more left than most of Texas. At least significant parts of Houston.
It's a shame, but Texas passed laws prohibiting cities from enacting anti-gun ordinances. They tried that at the Houston zoo. Went to court and the city of Houston had to remove the signs prohibiting folks from their concealed carry rights.
Needless to say, it's up to the business owners whether the want it or not. My lil ol pinion...if I were in business in Houston, I'd encourage concealed and open carry in my place. Businesses get robbed by the dozens a day in Houston.