Sorry it took me so long to jump on this post, But i regret to say, that I met so many Australians when I was Europe, I had lodging every night I was in OZ. Although, I did use the services of a bunch of hostels in the city core, Internet use, phones, brekfast, socializing that kinda thing, and did not have a problem at any. Here is a TP link to a whole whack of hostels in Sydney, you should be able to find everyting your looking for there.
TP's Sydney Hostel List
Enjoy Sydney, Its pretty wicked there!!! B)