No real decent places to play downtown. But just north of downtown on Airport Blvd is The Grand, formally known as Eric's Billiards. Its old-school pool hall. They have about 5 nine foot Gold Crown's and about 8 or so eight foot tables and a couple of bar boxes and some darts. Even a domino table.
4631 Airport Blvd
Austin, TX 78751
They have a 9ball tournament on Thursday nights. $10 starting at 7:30pm
There is also a Slick Willie's not too far south from downtown on Lamar Blvd. They have a Sunday night tournament starting around 8pm.