For a unique San Antonio experience without going to the riverwalk, try Rosario's in Southtown on S. Alamo, which is the King William district. Here's their web site:
www.rosariossa.com
I suggest the original Blanco Cafe at, 1720 Blanco, for breakfast the next morning, or Teka Molino on San Pedro just south of North Star. Like the Taco House further down San Pedro, I like the affordable neighborhood joints that have been around forever.