We are interest in all three because we want to get a well balanced picture of Australia. The main reason that I started this thread is that the country is so large that I am having trouble figuring out what to see. Great Barrier Reef , the Outback, Uluru, Tasmania - Where to go? How much time? Which cities - every one has something to see. This is as hard as seeing the US including National Parks, Hawaii and Alaska in one month.
Plan on being here for 6 months, Sirius, not a couple of weeks!
You will probably fly in to Sydney, and there is plenty to see and do there before you move on e.g. the Opera House, Harbour Bridge, The Rocks, Circula Quay and the squillion dollar homes of Point Piper (where our PM is happily set up).
Distances in the outback, which is hot, dry and a lot of the time featureless, are large and boredom can be a problem. I know from our around-Australia trip in 2011. Straight up from Adelaide (The City of Churches) to Darwin via Alice Springs and the splendid "Devil's Marbles" (Karlu-Karlu) is thousands of kilometres of saltbush, gibber, mesa ("jump-ups"), mirages, heat, dust and flies. West from Darwin and the very long and boring road to beautiful Broome (pearls, food, Cable Beach) via, say, bewitchingly beautiful (and remote) 80 Mile Beach, down to Perth via Ningaloo Reef (swim with whale sharks, coral snorkelling)... Perth is a very tidy and beautiful city with a spotless rail network and bustling city. The Nullarbor is borrrrrrring as a drive but the sunrise and sunset light will make you gasp.
Queensland and the Great Barrier Reef are well worth seeing (Brisbane). The further north you travel in QLD, the more remote and hairy it gets (pat a crocodile??)
Uluru will necessitate a long drive if you fly from, say Alice Springs (around 440km/one way). We found it exceedingly busy and uncomfortable with tourists buses cluttering up car parks. Kata Tjuta/The Olgas are a fair distance away and also well worth seeing (nowhere near as busy and cluttered), but the walks there ("Valley of the Winds") are on the strenuous side when you factor in the heat. Kings Canyon is jaw dropping; it probably will remind you of the Grand Canyon, on a smaller scale, but it too can be very hot and dry (you need to always pack lots of water on your walks anywhere you go).
There are changes afoot to Uluru visitation, including but not limited to, a proposed ban on climbing Uluru (visitors should not be climbing Uluru anyway as it is disrespectful to the traditional owners). It is also illegal to photograph Ulura from certain angles e.g. in front at the Visitor Information Centre, and especially behind (that is to say, all walks and car parks are at the front) due to cultural sensitivities. People have had their cameras confiscated doing this by roaming indigenous rangers.
Across Bass Straight in Tasmania, you could lose yourself in its Spring-time beauty. Cradle Mountain National Park is always busy (even in the frigid winter months), and will be busy in Spring (September-October). Cradle Mountain, Mount Field National Park (Tassie's oldest national park and close to Hobart) and Freycinet National Park on the calm East Coast all warrant visits and stays. Be aware that it is a long drive from Devonport where you get off the
Spirit of Tasmania ferry and desire to drive to Hobart down in the south (unless you fly direct to Hobart and skip the ferry, but it's an interesting experience, but not a cruise-ship experience!). A great place to spend a week or more and many, many choices for food. In the deep south of Hobart is the start of the South-West National Park (remote camping at Cockle Creek). The place to be if you like wild open spaces and less company, but if the weather turns, bunker down.
Canberra? Pass. It's bland and unserviceable as a destination, unless you want to keenly sit in on a debate in the House of Representatives at Parly House and watch them slug it out! Seriously though, it does have an interesting history and its demographics and geography make-up has unusual quirks.
I could fill chapter and verse about my home state of Victoria, but I think you will have a hard enough time with the rest of the States!