I've had issues with Uber's availability here in Columbus. I've used Lyft as a successful alternative and it looks like san antonio is a supported city.
The three rides I've ever taken have been great. Cheaper than the cab, and the app tracks the car on it's way to you so you know exactly where it is.
I'm an Uber driver myself in Atlanta, it's a nice little side gig. You should never tip, it's built into the cost of the fare. I plan on using Uber exclusively while in San Antonio. One thing to be careful of is the difference between Uber and Uber-X. With Uber-X you get a driver that drives his/her personal vehicle and is comparable to how much a taxi would cost. With Uber you get a driver in a suit that drives a black lincoln, they'll open the door for you and it will cost at least twice what a taxi would cost to get anywhere.
In Atlanta, you can't request an Uber-X from the Airport to anywhere, if you use Uber, you can only request a black car. I'm not sure if it's the same in San Antonio.
Hope that helps!