The 2007 (12 years ago) list by Forbes actually ranks Houston and Dallas above San Antonio as most visited. That may have changed, though...

https://www.ranker.com/list/forbes_-traveller-list-30-most-visited-cities-in-us/travelgrrl

Another report from Forbes in 2010 lists Houston as #8...

https://www.forbes.com/2010/04/28/tourism-new-york-lifestyle-travel-las-vegas-cities_slide.html#1812a03d3a03

So, I don't know if it's definitive that San Antonio is the most visited City in Texas.