As mentioned in the above post, Albtross Aero Club is definately the go. I recently posted our of HMAS Alba-trough to RAAF Pearce, but I know that plenty of civvies fly with the aero-club there, and they have reasonable prices.
Otherwise your next best bet would be to goto Albion Park (40min drive north of Nowra) and fly with AAP.
Any questions PM me.