Australia has a slightly different newspaper culture than Britain. The main weekend broadsheet comes out on the Saturday whereas in the UK Sunday is the main day. In Sydney you can pick up the weekend editions of the broadsheets which cover both Saturday and Sunday.
There are only two broadsheets in Sydney. The Sydney Morning Herald is more of a centre left paper, equivalent in politics and content to The Independent. The Australian is more right wing and fits in to the slot occupied by The Telegraph in the UK.
One thing I looked for when I first arrived was where to find British newspapers in Sydney. The local press is good quality but I really missed the large Sunday editions of The Observer or The Times.
Unfortunately I have never been able to find printed versions of these. The only option available are weekly tabloid format editions of The Guardian (Guardian Weekly) and The Telegraph (Telegraph Weekly) or the full version of the Financial Times.
The best bet is just to get used to reading the online versions. They are free, give up to the minute information and are easily readable on an ipad or laptop. It’s not quite the same experience as flicking through the ink covered sheets on a Sunday morning but the information is there.