San Antonio does have such a law on the books, but they will never enforce it. If they try, the state will come down on them so fast, it'll make their heads spin. It is both illegal and unenforcable.
Texas has a state sovereignty clause for firearms laws. After Federal laws, there ARE no other laws concerning firearms and the conduct thereof other than those passed at the state level. This was recently proven out when Houston banned gun shows in city limits and got sued. Houston lost. They then appealed it to a Federal court, which affirmed the state constitution's provision of state sovereignty in the matter, and told Houston to get lost.
San Antonion has never, ever enforced that law, and now they never will.
San Antonio was one of the cities I knew of (lived there a while) and I would be surprised if Austin did not have such a law. And I agree, the state law overrides the city law.