San Antonio without a car possible?

I have a connection in DFW on an upcoming trip and I'm thinking of stopping soley to visit San Antonio (I have been to Dallas and Fort Worth sometime ago). I do not drive, is getting around San Antonio easy without a car? Can I visit the Alamo using public transport? I will book a tour for the Alamo but the tour company tells me they operate the tour if there are enough tour participants otherwise the tour gets cancelled. This is why I need to know if I can take public transport to teh Alamo. Is two days, three nights enough in the city?

San Antonio without a car possible?
With no car I'd stay near the Riverwalk. It's 10 miles from the airport. I believe #5 bus takes you (40-50 minute ride). From Riverwalk it's an easy stroll to the Alamo which you can explore on your own. I think 2 nights/3 days is plenty of time for San Antonio.
San Antonio's Downtown and Riverwalk (safe for night strolls) area is compact and walkable, including the Alamo. IIRC, there's a purple Via bus which will take you to and from El Mercado (free). There are some moderately priced "lesser brand" hotels along the Riverwalk. You certainly don't need a tour or guide for the Alamo, small in scope and with good signage and illustrated explanations.
Riverwalk area is very walkable, and that would include the Alamo. Two days are plenty if you don't drive.

If you don't already have tickets to SAT, consider Greyhound Express. Yes, that Greyhound

They recently launched Express service in Texas between the four major cities, and apparently it's quite nice including wifi onboard. Unfortunately Greyhound bus stations are involved, BUT if you purchase far enough in advance, $1 fares are available. I checked, and saw some for mid July.

Unfortunately Megabus just announced that they will not be using downtown Dallas but Grand Prairie due to some issues, and that location is hard, if not impossible to get to using public transportation

Oh, it's about five hour trip, so quite a bit longer than if you are connecting and already past security, otherwise pretty good if you add up the time to and from the airport plus going through security.

Not sure why you don't drive, but San Antonio now has bicycles for rent downtown. That might be an option for you too
If you are not going to Seaworld or Fiesta Texas, one day is more than enough time to see San Antonio. Go to the Riverwalk, see the Alamo, look at the tower and eat some Tex-Mex. That's about 90% of the city right there.
Alamo took about two hours
The Alamo is a very small place. The river walk and touristy boat tour nice. Some of the better restaurants are a mile or so off river walk like rosarios ( best fish tacos) and easily walkable or on the central bus lines.