score:7
Ok, first of all there is a list of restaurants apart from the big chains which offer free Wifi as long as you consume something. Obviously you will have to make sure that these places are open and according to your taste. A cafe or pub might be more suitable than a sushi restaurant for long-term surfing.
Second of all there is a HUGE list of places with free wifi, and this list is maintained by an online magazine and much more detailed.
Upvote:3
After exploring for a few days, I've found some options.
Many local coffee shops offer free wifi, often as part of a 'complete a survey, get free wifi' deal.
The Gloria Jeans Coffee chain has free wifi.
Flinders Street Coffee has an Internode free wifi option, which I suspect is in several places.
Melbourne Central station and food court has free wifi.
the State Library and other libraries have free wifi.
Federation Square and the information center also has free wifi.