+1 to The Driskill Hotel. Don't miss it if you are on 6th. Just to see the beautiful lobby, or better yet head up the stairs, sit down on a cushy leather sofa, and order up a Shiner Bock or Fireman's 4 (two of the many local brews to choose from).
Also, the Gingerman pub (Downtown, but not on 6th) has about a bazillion beers on tap. If you head a little north you can find The Pint House where they make awesome pizzas and they brew right on the premises, in addition to having a great draft selection.
Edit: that's pint house pizza
http://pinthousepizza.com/
and no I dont work there... its just awesome...