Not Austin, but in DFW there's a local chain called freeplay arcade. Its a ~$13 cover charge and then unlimited gaming.
While not totally covered by a cover charge, there's also an arcade called Nickelrama. Cover charge, and then all games cost like 1-6 nickels.
There's a brand called Cidercade (used to be very affiliated with a cidery), they've apparently got a location in Austin as well. Similar story, $12 cover, all games included.