OP you want tropics, then you really need to be north of the Tropic of Capricorn :) That basically means, in terms of cities, Townsville and Cairns in Qld, and Darwin in the NT. They are hot and sticky for half of the year, and hot and dry the other half.

Brisbane has a humid subtropical climate, which may make the best major capital to suit your needs. It is cheaper than both Sydney and Melbourne, though I believe this is changing as it appears the city is undergoing some form of 'reinvention' to compete with its southern neighbours.

Sydney is also humid subtropical, though a little cooler overall than Brisbane, and less humid. However, Sydney is a vast city and the difference between coastal suburbs, and the western regions (also the cheaper regions) are quite marked. It can be 30 degrees and raining in Bondi, yet 40 degrees and dry in Campbelltown, which is where you can find cheaper places, even a 3 bedroom house, for <$400/week.

Melbourne has a temperate oceanic climate, though it doesn't appear to be able to make up its mind. You could wake up needing shorts, and come home needing a jacket and long pants. It's slightly cheaper to live in than Sydney, but not by much.

Adelaide, which is a nice city IMO, has a Mediterranean climate aka hot and dry. In fact Adelaide is the driest permanently inhabited city in the world (which is not saying much on the driest permanently inhabited continent in the world).

Perth also has a Mediterranean climate. However people are leaving the east coast for the relatively cheaper housing in Perth. I've been looking at places for my MIL and I can't believe how cheap Perth is compared to Sydney and Melbourne.

Canberra is full of hot air :P Seriously Canberra has a warm temperate climate, with 4 distinct seasons...one of the few Aussie cities to do so. It's hot and dry in summer, and you'll freeze your bits off in winter...being used to tropical weather that is. For some us it's not cold enough.

It terms of work, the most opportunities will be in the east coast capitals, especially Sydney and Melbourne, with Canberra being full of students and public servants haha.

Both Sydney and Melbourne has extensive public transport networks, so even from the outer reaches of both cities, you'll generally have no drama getting into the CBD, it just may take an hour by train to do so.