True for Sydney, false for Brisbane.
In Sydney it's because East means harbour and/or beach.
In Brisbane east is flat industrial wetlands, West is hilly with views/breezes, with the exception of Clayfied/Hamilton/Ascot. However, if you travel further west towards the city fringes, this reverses quite quickly.
I'd say on balance true for Melbourne, but I'm not enough of an expert to say for sure.
Generally I would say that the desirability of certain areas comes down to :
- topography (low, hot bad, hilly, views, breezes good)
- orientation : people (in general) like to live on or near the water, assuming the water is clean. Areas that face into hot sun are less desirable.
- history : sometimes older parts of cities have bigger houses and land, and are more established.