Have a look in the Dunnunda GA section. There is quite a lot of advice there on sydney flying schools
I have a FAA PPL, and am converting to an Australian one. I had a look at a a few schools at Bankstown. Personnally I am going to use Curtis Aviation at Camden (which is another 15 minutes further out of Sydney than Bankstown). They were very well informed about the conversion and have a variety of airplanes (well maintained & tidy) to learn in. They have quite a good website.
having never lived in Melbourne I cant comment on the weather, but I think Sydney would be just fine. Most days here are clear blue skies
Hope that helps, but you may want to post your question in the dunnunda section, but would recommend that you do your research.
G'Luck