I prefer to fly, but the drive is not bad. As kale75 said, it’s about a three hour straight shot down I-10. I’ve flown it hundreds of times and driven it more than a hundred times.

You might consider leaving a little earlier and making a pit stop for lunch at City Market in Luling. It’s a very minor detour and the barbecue is excellent. I believe they only take cash.

I’d keep the rental car for the full duration of your time in both San Antonio and Houston. Public transportation is poor in the sprawl of Houston and even less useful in San Antonio.

You can probably find a rental car code that doesn’t penalize you for one-way rental. If you don’t know one already, you might try Autoslash.

Lastly, if you don’t want to fly and don’t want to drive yourself, Vonlane offers executive bus service (comfortable seats, free wifi) from downtown San Antonio to downtown Houston: https://www.vonlane.com/