In Australia, the majority of coffee places are going to be non-chain, small cafés. Also, most places will only sell you espresso-based coffees like lattes, cappuccinos, flat whites, etc. Don't bother asking for a brewed coffee.
For espresso-based coffee, there are a number of good places. Overall, most places are pretty average, but Australians think it's world class. 😛 In fact, I'd say most of these cafes are only slightly better than Starbucks, but ALWAYS significantly cheaper, so that's a plus. They're still far better than Canada though.
If I want normal brewed coffee, I go to Starbucks. Unfortnately, they're my best, and only, option for brewed coffee if I'm not home. 😱 There are a few other boutique coffee places that I go to for "brewed" (i.e. plunged, siphoned, etc) coffee, but these are SERIOUS coffee places, where you either need to dress up in a sweater and dress pants (with work in hand) to get in through the door, or perhaps skinny jeans and a dumb haircut and pretend you're doing something artistic. This implies, of course, that I pay out the ass for a cup of the black stuff, but it's something you need to live with when you're here. 😱
In fact, brewed coffee here costs almost as much as a latte/cappuccino, and I'm so used to $1.60 coffee (Tim Hortons....) in Canada that I now find myself more and more unwilling to buy.
At work, I'll use my plunger and make my own. 🙂