This is Australia, so free Internet connections are a rare and beautiful thing. Some of the CBD cafes are starting to provide wifi, but you need to ask for the key.
McDonald's started rolling out free Wifi in Sydney. This is huge for Australia, check it out!
383 Kent Street has a fab coffee shop in the foyer. Its the MYOB building and while I didnt WIFI there was a sign that says there was free WIFI. They make great tucker and coffee too!
There is a free WiFi service called uConnect in lots of locations around Sydney - mostly cafes, but also in places like the Kings Cross Library. Use this page to see where it's available:
If all else fails, there is always the Apple Store in Sydney.
Tower 1, Darling Park, 201 Sussex Street, Sydney has a free wi-fi in the foyer... (or at least used to until early this year when I worked in the building)...
Alternatively, try a McDonald's in the city....
Lobbies of Westin Hotel (at Martin Place) or Sheraton on the Park Hotel.
The Daily Express (Circular Quay, right beside the ferries) offers free internet with any purchase. Great fish and chips!
Espresso Bianco, 383 Kent St, Sydney. Good food, coffee, service, and free unwired.. genius
Half the cafes/pubs in Newtown have free Wifi.
If you walk up king st most of them have signs at the entrances advertising it.
McDonald's at the Sydney Entertainment Centre, McDonald's on the corner of Pitt St and Park St and McDonald's near Apple Store in George St near King St and Glebe Library plus other Sydney City Libraries have free wifi.
Clipper cafe in Glebe
Toast Cafe, 45 Reservoir Street, Surry Hills.
Ask the staff for the code.