I was in the Montesino a few times over the summer and it was busy and well run. The tournaments will prob be slightly lower than your price range unless there is a festival on. You can check near the time at
http://www.montesino.at/ .
The other main room is the Concorde, I didn't get there on my holiday but have been many times and it is also well run.
Their calendar appears to have the Montesino tournies in it as well. The Vienna comps are "Wien Simmering".
http://www.ccc.co.at/turnierkalender/You will need photo id to sign up at both clubs.