The Murdoch Astronomical Society (which no longer exists btw, they merged with ASWA) used to go out along Brookton Hwy, but a lot of other people wander around in those areas, not always nice people up to legal activities, so I would only be heading out there with a friend in tow.
ASWA currently has their deep sky meetings in Parkerville but it's not a particularly dark site. In the long term ASWA will have a permanent site in the Wheatbelt about 2 hours from Perth - it's under development at the moment and hopefully the pen-pushers in Perth who are holding up the paperwork at the moment will pull their fingers out soon so we can get going with it!
Another spot to try is out along the road to York on the side streets. I used to use one with some friends but can never remember the name of the road.
A lot of locals just take a drive one day to scout out good spots in the forest, and that might be your best bet.
Don't go south, as the others have mentioned, and don't go to the Gnangara pine plantation unless you like living dangerously.