Naxos !!!!! i cannot stress this enough,,,-

Sure see mykonis and santorini but after spending 10 euros on a drink, and 30 euros for crappy dinners , you will breath a sigh of relief in the beautiful isand o f naxos. Peole ar e charming , beaches are pristine, and no Starbucks or Loius Vuitton stores..

Honestly, I'd reduce that time in Athens unless you plan to live in the museums (nothing wrong with that). I find Athens noisy, crowded and likely very hot in early September. Aside from the islands (and in 21 days I'd try to see more than one island group), places like the Peloponnese and the Pelion Peninsula are very interesting.

You have enough time to see quite a bit of Crete on this trip. Why not go for it? Naxos is really interesting and I'd much prefer to return there than to Santorini or--especially--Mykonos.

Although I haven't been there myself, I'm convinced by everyone's raves about Nafplion.

I agree with the suggestion of Naxos as one of the islands you should visit in the Cyclades. When we traveled to Greece in 2012, we only had 8 nights. We spent 2 in Athens, 2 on Santorini, 2 on Naxos, and the final two back on the mainland in Nafplion.
I relied heavily on the Greece travel blog of Matt Barrett to plan that trip. Such a wealth of information, presented in such an entertaining way. Have you found it? Here is a link:
http://www.greecetravel.com/matt-blog/

Congratulations on choosing a wonderful time to visit, the crowds have gone, the weather still will be great, and the sea will be superb!! Everyone here has good ideas, and I agree with lots of them, and will plunge right in with my own "tweak" of your trip.

FIRST: Do NOT start with Athens. Yes, you'll be totally exhausted from that gruelling journey from Australia. But why go into Central Athens twice, checking in/out hotel, taking bus/taxi etc???? Waste of Precious HOurs!! Have a strong espresso on arrival, and do one of 2 things (1) FLY to FARTHEST POINT afternoon flight to your FARTHEST island destination & you can have 1st sunset on a harbor! Then island-hop back to Athens... or (2) DRIVE or BUS** to FAB PELOPONNESE "Gem" -- NAFPLIO, only 2.5 hours on modern hi-way, is on a Peninsula, totally surrounded by water, called by Greeks THE most Beautiful Old Town in the nation. Spend 3+ days in area, then bus/drive back to airport, THEN do the Domestic flight to farthest isle.
**If u are tired, this is Great choice; airport X93 bus to KTEL (Intercity)bus terminal, then an a/c resrved-seat bus all the way. Nafplio & area is gorgeous for history, culture, food, swims; study this NONcommercial super website: http://www.visitnafplio.com While there u could rent a car for a day or so to visit famous ancient sites: Mycenae, Epidaurus etc.

SCENARIOS:

1 - ATHENS - FLIGHT to CHANIA, CRETE • 5 days Crete (rental car for 4) ending in Heraklion • AM Ferry to SANTORINI (2-3 days) *Ferry 3pm to NAXOS (5 days - inc. 1-day excursion to Mykonos) • Flight (45 mins) or Ferry (4+hrs) to Mainland • Drive or BUS to Nafplio (3 days) • Last 3-4 Days ATHENS

2 - Basically a "Flip" -- Bus/Drive to NAFPLIO (3 days) - Back to Airport FLY to CHANIA - ferry SANTORINI - Ferry NAXOS - Ferry or Fly ATHENS.

-- A variant on both: if you truly are exhausted/dizzy on arrival, there's a little local B & B in an olive grove, w. a pool, where you could swim, crash, have early night -- then start EARLY next AM (bargain flights!) or do bus or rental car for version#2

This gives you variety and adventure (NAXOS is great for hiking, so is Crete). You have time to get this right. Warning -- figure out your "logistics" (flights, bus, ferries etc) BEFORE booking accommodations ... except for 1: it's wise to book a place in Athens for the last 2 nights; Sept gets v. busy... and once you get into a hotel you can "tweak" it a bit (add/subtract a day).

PS: Don't rely solely on Internet websites about Destinations; many are designed just to draw tourism/make ad $$s, so they show only the "beauty shots", nothing about downsides. You have good libraries in Australia, run over & get a Lonely PLanet & Rough Guide to Greece, browse a bit. Guides make their reps by giving full picture, not just "eye candy".

My Apologies !!!!! I did NOT mean for those Scenarios to be made GIANT Size ... and I can't seem to get them reduced! I have tried everything. Please do not infer that I am that Forceful about the idea ... I just can't master the edit function!!! --- TJ

If you are feeling that you have too much time planned for Athens then you are probably correct. There is lots to see out on the islands.
Many people suggest you find a connecting flight to an island immediately on your arrival in Athens. We travel from the west coast of Canada and the trip is pretty close to 24 hours total travel time but we drink coffee and go on adrenaline and fly to an island. Thats the best place to get over jet lag.
You need about two hours to make a connection.
Here are a couple of things we have done: Fly to Chania Crete. It is a lovely city in the west with a Venetian era old town and harbour. Relax and get over jet lag while you explore the city. Then consider day trips. Some suggestions: The famous Samaria Gorge hike is a full day 6am and getting back around 8pm. Ancient Aptera still an active Archeological dig site. Take the day boat excursion to the beachs at Balos and Gramovossa which includes a pirate fortress. Falasarna has a good beach and there is an ancient site as well. You can do a day trip to Rethymnon. It has a small harbour and a nice old town area plus the Venetian Fortezza.
Western Crete http://www.flickr.com/photos/stanbr54/sets/72157632115757899/

Chania http://www.flickr.com/photos/stanbr54/sets/72157632117917828/

When you have seen everything you want to then head south to the Lybian sea. There are villages dotting the coast. This area is the center of hiking on Crete and has mountains and sea vistas, You could start at Paleochora which has a nice sand beach. From there you can take the coastal ferry to Sougia then Agia Romeuli where the Samaria Gorge hike ends. There is a second ferry at Romeuli that continues east to Loutro and terminates at Chora Sfakion. There is a hiking trail all the way from Agia Romeuli to Chora Sfakin that includes the wonderful sweetwater beach.
Ferry trip Libyan Sea https://www.flickr.com/photos/stanbr54/sets/72157653434073393
Crete Libyan Sea villages https://www.flickr.com/photos/stanbr54/sets/72157645487373222/

This can easily take up to two weeks to do. That leaves you a few days to ferry to Santorini (which in my opinion is a must see destination). Santorini is very expensive for dining and accommodation but the view over the caldera is worth every euro. Be sure to get a hotel with a caldera view.
Santorini http://www.flickr.com/photos/stanbr54/sets/72157632154800782/

Depending on the best connecting flight in Athen you can fly to Santorini then ferry to Crete. The port is at Heraklion which is a very busy city but it does have Knossos and the museum plus an interesting Venetian port and buildings in the center.

Second alternative is to fly to Santorini then island hopping back toward Athens. We generally spend 4 days in Santorini (thats all our budget can take) but others can spend weeks there. By this time of year you can stay as long as you like and leave when you feel like it. We go to Naxos. It is like a smaller version of Crete. It has a lovely main town with its 6th century BC Portera, waterfront promenade, back alleys all topped off with the Venetian Kastro. Naxos has great beaches and mountain villages. We spend a week to two weeks on Naxos every time we go to Greece and we still find new things.
You can take a boat excursion to Delos and Mykonos. That way you get to see Mykonos but don't have to pay the exorbitant prices.
Naxos Town http://www.flickr.com/photos/stanbr54/sets/72157632094558042/
Trip around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/

If you still have some time left Paros just an hour ferry ride away is also well worth a visit for a few days.
Make sure you get back to Athens for at least a day before your return flight.
There are other great places to visit Like Nafplio and the Peloponnese
Nafplio and Peloponnese http://www.flickr.com/photos/stanbr54/sets/72157632094108982/

Apparently Janet and I are thinking the same way

Let's confess, stanbr ... we 2 are actually the same responder -- a "Greece-O-Mat" robot operating out of 2 locales, to avoid detection!!

Thank you all soooo much for taking the time to post these ideas. They are extremely helpful and we will definitely be taking your advice. Thank you😃👍