I've been to all of those cities and here is my opinion of them, starting in the north:
Cairns is a beautiful place with a population of about 80,000 people. Any work there is mainly seasonal as the "wet" season is uncomfortable (Nov to March) and the place does get hit by the tail end of cyclones occasionally.
Brisbane (1,500,000 people) has probably the most reliable climate of all with temperatures around the mid twenties all year round. Not sure about work there. Rents are reasonable.
Sydney (4.500,00 people) has got to be one of the most difficult and frustrating places to get around I've ever been. Rents there are horrificly expensive as well.
Melbourne (4,250,000) would be my pick as it has pretty well everything going for it with the exception of the winter weather which I would best describe as similar to Vancouver except not quite as cold. Rents are not as bad as Sydney but still a little high all the same. For work it shouldn't be too difficult to find something, especially if you're looking for casual work as there always seems to be a shortage!
Adelaide (1,500,000) is known as the "City of Churches" and is quite pretty, rents are relatively cheap but work's a little harder to find. There is also a saying in
Australia that they switch Adelaide off at 7pm - it's pretty quiet in the evenings.
Perth's a great city (2,000,000), there's a lot of work there and rents aren't too bad. The biggest problem with Perth is that it's the most remote capital city in the world and if you're going to Aus to do tourist things it's the wrong place to base yourself as travel to and from there is expensive - similar to travelling across Canada.
Hope this helps, good luck!