Where to go depends a bit on your own tastes too... There are some excellent modern fine-dining places in both Melbourne and Sydney (don't know about Cairns, I'm afraid), but also many less fancy establishments serving outstanding food.
Dining out never (?) costs as much in Aus as in the US for comparable or better fare and ambience. Sydney is perhaps best known for modern Pacific fusion cooking, while Melbourne tends to be more modern traditional, with strong interest in Mediterranean food (though there are excellent restaurants from a number of Asian cuisines as well).
I'd suggest picking up a 'good food guide' on arrival in each major city and looking at what takes your fancy. There are very very few places that would require a booking more than 24 hours in advance.
Happy to answer any follow-up questions.