This is about as authentic as one can get. Don't let the fact that it is on the east side deter you. Go get it, it's GREAT!
This place gets 5 stars from me. I first went to it when I was a junior or senior at UT back in the early 70s. Authentic atmosphere, right down to the pictures of JFK and the Pope on the wall. I think those photos are still there. Try the cabrito, along with a double helping of Spanish rice. You won't be disappointed.