Check out
www.transperth.wa.gov.au/ and enter in a journey planner from Curtin to places like, Melville (don't know the streets there) and Pelican Point (much closer) which is on Hackett Drive, opposite UWA, which is good on anything with south in it, best on a SW - Melville is also good on a westerly.
Concession bus tickets cost about 80c.
Getting to the coastal spots without a motor is more tricky. Best thing is to post on this forum to see if you can share the costs of driving with someone. Lanclin is only 1.5 hours max, and is a wicked place to ride, and can get bloody windy. The backpackers are good to check to see if someone is doing an extended trip away - catch a ride out of Perth, and then hook up with someone else coming back. There are buses too of course, to the bigger towns, but they aren't going to be going exactly to the spots you might want to go.
There are some great coastal spots in Perth too, although the waves aren't all that. Flat water at Woodies, south of Freo, but a bitch to get to without wheels, otherwise the river. Hope this helps.