As a Perth local, I thought I'd drop in a few suggestions/tips.

Fremantle is certainly worth heading down to, it's really beautiful and has a lot of Perth's history, so there's lots to see. Make sure you take a night tour of the Fremantle Prison, the day tour isn't as much fun. The prison was in continuous use from the 1850s through to 1991. http://www.fremantleprison.com.au

In the evenings, you've really only two places (as has been mentioned) The Court Hotel and Connections (Connies). They're only really busy on Friday and Saturday night, though The Court on Sunday evening is pretty good. Being there's so little choice of venue in Perth you'll get pretty much all types at both these places.

If you like bushwalking then head out to Mundaring (about 45mins drive inland) and have a look at some of the Bibbulmun track. It runs some 1000km down to Albany, but there's plenty of little day trips you can easily take along sections of it. http://www.bibbulmuntrack.org.au There's lots of other interesting short tracks around Mundaring as well.