I grew up in Darwin and personally I would really recommend against visiting in February, unless of course you like 24 hour a day saunas. It is very humid and hot, d@mn hot, and there is no relief at night (although an airconditioned hotel room will obviously take care of that). Beware, the maximum daytime temperature may not look all that high but it doesn't tell the full story.

At that time of year you also cannot swim in the sea because of the box jellyfish (which we used to call sea wasps) - they WILL kill you with their tentacles (from memory the poison shuts down the nervous system and you can't breathe). Even a very minor sting causes unbelievable pain which will revisit every now and then for years (my brother was stung once).

It's also a really long way from anything. It is the stepping off point for a trip to Kakadu and a few other places, but at that time of year (the Wet Season), chances are high that the roads will be flooded and you will either not make it there or not be able to get back.

Having said all of that, it is perhaps worth taking some of what I have said with a grain of salt - I haven't lived there for almost 25 years but I'm pretty sure I still have "issues."

Perth is nice, but again at that time of year it can be really hot - way over 100F at times, and Perth has the same problem of being a really long way from the east coast. Brisbane will also be humid, but not to the same debilitating level that Darwin reaches. It's a good option for that tropical experience with the benefit of being relatively close (in Australian terms) to other significant attractions like the Great Barrier Reef, Gold Coast, Sunshine Coast, Surfers' Paradise, a number of rainforests and the various Queensland islands. It is also only an hour or so flight from Sydney.

With only seven days I would probably stay on the east coast - plenty to do in Sydney, Brisbane and their environs.

Have fun!