Haven't lived in Perth since 2008 (and we rented while there) but suburbs that are close to the beach, city, and train all fall within the western suburbs - the most desirable in Perth; Nedlands, Claremont, Mosman Park, etc. You could try looking a little further north, although the train line is further inland at that point. You'll get more for your money though to the north, and the beaches at Waterman's Bay, Hillarys etc are nice. As we lived north of the river in City Beach I have no idea of the best locations south of the river. If you are up for cycling in to work, it was a 15 minute drive or a 30 minute bike ride to the city from City Beach for my husband when we lived there. A little closer to the city in the same direction was Subiaco (great for younger people, lots of restaurants etc), and it's close to Kings Park for the dogs. Hope that helps a little.