Good place to live for families without a car?

Hello! We're a family with a 6 y.o. daughter who just moved to Perth. We're looking for a safe suburb that we can have all the facilities close (school, market and bus), since my wife can't drive. We don't want a big place, a 2 bedroom apartment would be great for us, since it's easier to clean.
I know how hard it is to find a place like that, and that's why I'm asking! What are your thoughts??? Thanks!!!