City Deli in the new part of the Canberra Centre has wifi and I'm pretty sure its free but you have to be in the know. From memory they had a little sign near the coffee section advertising it. Normally I'd just check with my son as he works there, but he's OS at the moment. I'll check next time I'm in there.
I'm thinking of getting an iPod Touch so knowing where the wifi hotspots are around town would be would be handy.