Basically, San Antonio is the "riverwalk". There's loads of bars/restaurants up and down the river. Good food, pricey drinks and great people watching. Here's what comes to mind first:
The boat tour is cool... And, that mexican restaurant with the umbrellas is amazingly good:
http://www.casa-rio.com/this thing is pretty popular.
If ya like golf, La Cantera is a really nice place to play that allows public access.