There's casual play almost every day of the week in Austin.
Mages Sanctum has X-wing Academy on Tuesdays, and regular play on Wednesdays.
Dragon's Lair has casual play on Friday nights.
Whose Turn is it has casual play saturday afternoons.
Tribe has casual play on Mondays iirc.
I believe Mothership has open play every Sunday, which once a month is a tournament.

Also, check out Austin Xwing Squadron on facebook - most players are more than happy to help out new players.