Traveling by airplane is not always necessary if you're coming from somewhere else in Texas.
We usually drive from Houston. If you are doing so it is an easy shot on I-10.
If you're coming from Austin or Dallas it's just as easy a shot on I-35.
There are really interesting places to stop on these roads. Plenty of good resting places and shops. Very safe (in my opinion).
If you are planning to explore more than just the Riverwalk, then I would recommend investing in your own wheels for the trip. In our case, we chose to drive down from Dallas, but there are also plenty of rental car options in and around San Antonio. Several of the downtown hotels also offer rental cars through various providers, so check with your hotel if you do not already have an advanced booking.
Once you're in San Antonio, the best thing to do, unless you only want to stay in the river area, is rent a car. This isn't a city where you can wave down a taxi and quickly get to where you want to go for a few dollars. Parking is abundant and drivers are more than a little friendly. You can easily arrange to pick up and return your car at the airport.
Interstate 10 runs the entire length of Texas between Houston and El Paso. I Was lucky enough to drive this entire route in 2006, but to break up the journey, I spent nights in Houston, San Antonio and El Paso.
I-10 cuts across southern Texas from Louisiana to New Mexico covering a distance of some 879 miles. Out in West Texas the speed limits climb to 80 mph during the day (65 at night) and you will see a few trains, windmills, and not much else for miles and miles.
One thing i noticed about driving around in Austin and San Antonio was that EVERYONE tailgates and drives fast. I was a nervous wreak driving on the highways in Texas. I was in the car with locals so they did most of the driving. I noticed first that my cousin was driving like that, so i mentioned to her that she was tailgating the car in front of her. She told me "maybe thats why everyone's always stepping on the brakes."
We happened to see a week-end special offered by Advantage car rental. Their shuttle picked us up at the airport and took us to their lot which was very nearby.
We got the Sebring which was a sporty car.
We kept it for one day and traded it in on a van that had more room to accommodate the 5 of us.
We liked the new van but the engine light came on and stayed on so we took it back and exchanged it for another van.