I just checked a currency calculator. The US dollar now get 1.28 Australian dollar. I thought this might help you as you look at prices.
You may want to consider flying into Sydney and then back to the USA from another city such as Brisbane. Here are the routes available http://www.traveller.com.au/flight-routes-australia-to-the-us-the-best-and-fastest-flight-routes-to-the-us-and-which-airlines-flies-them-gttz3u the article is few months old but is a good starting point.
I would suggest you not try to pack too much into a short time. Remember…your travel time to and from will take up 1 1/2 Days each way. Then you have your conference. So that could encompass almost a full week together…right?
My kid has been to Sydney and she says…there is plenty to do and see there. The one thing she wishes she had had the time to do was a side trip to New Zealand…but that wasn’t in the cards…she wasn’t there long enough.
My son lives in Sydney. I was happy when I visited there last July to spend a little over a week in the city. There are great museums and parks to explore and wander. The gardens near the opera house are amazing. We went on the harbor cruise, whale watching, to the Blue Mountains, Bondi, and places on the ferry. I disagree with someone upthread who said public transportation wasn’t good. We took subway and trains multiple places and the stations are beautiful. I plan to go again in May. I plan to go to Sydney and then Tazmania or the Great Barrier. New Zealand is on my bucket list but many tell me don’t bother as I will only have about 5 extra days away from Sydney.
Melbourne & Sydney.
Stay as long as feasible, since this could be a once in a lifetime trip.
I’m envious.
Melbourne !
I prefer Melbourne over Sydney but I am not sure about that as a tourist. I think going north, or going bush would be more of a thing. Melbourne is just a delightful city to be in, and throw in the Great Ocean road for sure, but it is just another city. As OP has the city NSW experience, Australia is really the place for beach, bush, outback. If she had the $$, I would concur Uluru, and head at least towards FNQ. Check seasonal weather issues for beach especations. It really is about how adventurous is adventurous.
A note about Uluru: it is in the center of the country, very remote, and extremely expensive to get to and stay at. The last time I looked, there is only one vendor who provides lodging. We’ve been to Australia twice, and DH has been there two other times for conferences. Have not made it to Uluru.
Will write more later.
Never been but every person I know who has gone on to see New Zealand says they would spend all their time there.
One of my high school friends has earned significant wealth and, although he has small offices all over the world, he choses to live in New Zealand & commute when needed to London, NYC, San Francisco, Moscow, Singapore, and another location or two.
I liked Australia; I loved New Zealand.
New Zealand is on my bucket list but if I go I have to go with Mr R. It’s his absolute dream. He’s been obsessed since LotR.
I’m an Aussie - congrats on snagging the trip of a lifetime, and free airfare to boot! Stretch as long as possible. Two weeks is just not enough time. Any way you could telecommute for a few more days?
You’ll lose 3-4 days in travel (remember, you lose a day getting there, in essence) and recovery. The trip is brutal on sleep patterns/jet lag. Expect to be up in the middle of the night for a few days.
Are you leaving from the West Coast or East Coast?
Here’s the deal: Australia is the size of the continental U.S. You wouldn’t try to see all of America in two weeks; you’d concentrate on a couple of areas and hope to do the rest later. Problem with Oz is that most people never get a later. Hence the encouragement, again, to get more days for your trip.
In Sydney: if you’re adventurous, the Sydney Harbor Bridge climb is unforgettable. Downtown - walk from the Opera House to the botanical gardens. Also, Taronga Park zoo (city is the backdrop), the Rocks historic area downtown, Manly Beach via the ferry, Bondi for the surfers clubs (it’ll be spring then; you’ll have perfect weather) - beaches in general are sublime. Darling Harbor for shopping as you’re prepping to leave.
The closest other city is Canberra, but even though I spend my formative years there, honestly, you can skip it.
I’d try to get north to the reef, but it’s a long haul - about 12 hours. You’ll probs have to pick either the reef or head in the other direction, to Melbourne. Melbourne is about eight hours overland; longer back along the coast road, which is worth doing.
Unless you’re heavy into the ocean/snorkeling etc, I would pick the other direction, for Aussie-specific sights. See Melbourne/ drive the Great Ocean Road/ take a (car) ferry to Kangaroo Island. My parents had their honeymoon there and it is AMAZING - penguins, seals, wallabies & roos, koalas etc - nature to die for.
Skip Uhluru. I was born in the middle of the Outback and while it’s also stupendous, again, you can’t do it in the time allotted.
If you head to Melbourne, you MUST try to catch the Aussie Rules footy. You will thank me 
Let me know if I can be of more help. I LOVE my country
ETA: Almost forgot: Borrow or buy Bill Bryson’s “In a Sunburned Country.” Best book to distill the essence of Australia for an outsider.
We’ve been to NZ twice. First time was in conjunction with AUS and we spent nine days in each place. Nine days does not begin to touch the magic of NZ, esp the South Island. We got on the plane home and I said to DH that we could return for three weeks and not repeat a thing we’;d done the first time. Second time we were there for 16 days and spent almost all of our time on the South Island. You will ABSOLUTELY want to do the Glenorchy drive. There is LotR stuff on both islands. We want to go back again. You will love the thermal pools.
For a first-time AUS trip, I’d do Sydney and then head up to Cairns/Great Barrier Reef area, mainly for the different between city and tropical. We didn’t do the Opera House tour, but were able to walk around inside and get a sense of it. The parks nearby are lovely. Hyde Park Barracks was worth the trip. Agree with everyone who says to take the Sydney Ferries; it’s a cheap and easy way to see the Harbor and the surrounding area. There is a walking path (3km) from Bronte to Bondi Beach. There is also public transit. Went to the Australian Museum, too. Everyone wants to walk along The Rocks (expensive restaurants and hotels, great view of the Opera House).
We stayed a little south of Cairns in a little cabin 50 feet from the beach. Came with a mini kitchen, deck facing the water, and lots of solitude. Heaven. We also went to Townsville and did Magnetic Island, and also did a sea kayaking trip (about five hours); this was in 2005. Our favorite part of Australia is Kangaroo Island, off the coast from Adelaide. Brutally hot in the summer; gorgeous and cool in September-October. We did Melbourne and the Great Ocean Road two years ago en route to Adelaide. Lots of driving; the scenic part of the coastal drive is actually from outside Melbourne down through Peterborough.
We went to Tasmania two years ago – LOVED it. Was not sure that was going to happen. We were there in September and the weather was lovely. In December/January, it’s hotter than h*** and you get a better sense of why it was a penal colony.
September is a lovely time – it’s not too hot, not too cold.
Wow, thank you all. Especially @Gatormama !
This is a lot to take in so I’m still processing. Flights weren’t as bad as I had initially thought (a quick search said $2.5k but finagling dates had it about half that). My funding is in a block grant so the lower my prices go, the further I can stretch.
Also the reality of 24 hours of travel is finally starting to sink in. My body already hurts thinking about it 
If you can finagle a business class seat, @romanigypsyeyes, I’d do it. Lie-flat seats make all the difference for me. (Thank goodness for DH’s FF miles! He sits in Economy Plus so I can be upfront.)
Agree with gatormom’s post.
Definitely get as much leg room as you can. Even premium economy can be expensive so if there is seating such as economy plus on Delta, spring for it. Set a price alert on Kayak or other such sites.
My reading list suggestion with a women’s study emphasis are the books by Jill Ker Conway. https://en.wikipedia.org/wiki/Jill_Ker_Conway She wrote 3 books about growing up in Australia, grad school life and early career, and her presidency of Smith College.
There’s a time during the taxiing announcements, at least there was on Qantas, when the flight attendants would say “and we’re sorry, but federal regulations prevent us from allowing passengers to lie on the floor” – and everyone laughs… 15 hours in and you are BEGGING them to let you lie on the floor.
Last time we went back, we did it with my D19. She was a toddler. It was a nightmare.
Thanks so much for your post, though - it’s made me decide that even if I have to sell a kidney, I’ve gotta get my kids over to see my home - maybe for a graduation trip next year.
Jill Ker Conway is a magnificent writer. Also enjoyed “In a Sunburned Country,” but in a completely different way.
If you decide to go to Uluru, there are a variety of price options for the accommodations - luxury to pitch your own tent. But even the “cheap” ones aren’t truly cheap. We stayed in a hostel-type unit and paid for all four bunks so as to not be assigned a random roommate. Almost all (if not all) accommodations there are through https://www.voyages.com.au/
Ok need advice from experienced fliers: what’s the difference between premium economy and business? Business looks to be about triple the price.
I have no idea what premium economy actually means IRL.
Premium economy usually means 4 inches of extra leg room compared to regular economy. We flew United to Taipei (non-stop), and it makes a difference on 14 hour flights!!