im originally from sydney and went to school in alexandria. The southern suburbs out to brighton le sands and Kogarah are really nice areas and not far from alexandria.
if you really want to stay closer in to the city, then try glebe and surrounding areas. Its got a real old world charm to it and is not far from a maternity hospital. If you go slightly further west there is Petersham and Leichardt which are a bit more leafy in some areas.
with regard to 'safe' areas... not sure about that. I grew up in waterloo and its not considered a safe area but i never had any problems there...perhaps knowing the locals helps, but i think overall crime is prevalent in most places.
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