You're skipping Japan... Then its hardly "around the world" is it?
Dunno, seems pretty sensible to me
and I've been "around the world, not including wherever rob_japan lives" as well...(although it was, ahem, "several" years ago).
Sydney - try and get up the coast to somewhere like Port Macquarie, which is classic beach Australia. But Sydney is one of the most stunning cities in the world.
Alice Springs/Darwin - try to get out to the Olgas and go canoeing in Katherine Gorge with the crocs (little ones!). Then go and see the big ones in Kakadu (where Crocodile Dundee was set).
Adelaide - kind of a boring city but good scenery around it. In those days you used to be able to pick up farm work around the River Murray, if you need to earn money (picking grapes and fruit). Flinders Range is a must, and Coorong National Park is also stunning.
Queensland - northern Queensland is what I remember best. The south is a stretch of built-up beach resorts (the "Gold Coast"). It used to be interesting to get further up north than Cairns (which was also a big backpacker hangout in those days, filled with Swedes
).
In the end I decided to spend more time in Australia rather than trying to rush around Oz/NZ. As you can see, I didn't get to Victoria or Western Australia, but still spent 4-5 months there (and 1 day in Auckland!).
That would actually be my advice. Try to pick some places where you stay longer and can appreciate the time there more rather than trying to rush around and see everything on a list.
As far as the other destinations went, my route was a bit different from yours (Alabama, SF/Washington State, Hawaii, Fiji, Oz, NZ, Singapore, Athens) but I still managed to miss out Japan...