There are loads of Internet cafes in all the big cities and popular travel destinations. Count on spending around $4 an hour.
Wireless access is harder to find outside the big cities. Melbourne and Sydney have excellent WIFI access through
Boingo, which costs USD $21.95 per month. Adelaide also has brilliant WIFI access across the city centre and the Queen Street Mall in Brisbane also has WIFI access. In Cairns you can get free WIFI access at the Coast Coffee shop on the Esplanade.
There are also WIFI hotspots in Starbucks, Gloria Jeans Coffee and McDonalds that are run by mobile phone companies like Optus and Telstra, however these have very expensive changes. It is best to stick with the Boingo hotspots wherever you can find them.
A lot of the Boingo WIFI hotspots are run by
Azure Wireless an their website is often more up-to-date than Boingo's if you're looking for the addresses of hotspots.