One lovely little op shop a lot of people don't know about is the one at the Earthwise Community Centre in Subiaco. Although it's been running since 1991 it's something of a local secret! If you haven't visited already, the Earthwise Community Centre is a real gem, and is surrounded by lovely communities gardens decorated with sculpture upcycled by local artists. I'm not sure what hours they're open but take a look at this webpage for more information: http://earthwisewa.org/pages/opshop.html
Unfortunately, I haven't been in Perth long enough to find an op shop! I visited friends for a week, somewhere in W.A. then 1 day on a cruise. The other day on another cruise we didn't catch the train up to Perth.