Athens, Naxos, Crete, Athens

Putting all the Athens night at the end is more efficient, i.e., save one hotel move in move out cycle.

I would fly onward to whichever island you choose. Having to get from the airport to the ferry port is not what I would want to do after what presumably will be an overnight flight.

Yes, it’s wise to put all your Athens time together at the end of the trip. Give yourself a couple of hours after arriving in the Athens airport, and then fly to Naxos for 4 or 5 nights.

But rather than Crete, I’d suggest going next to Amorgos. It’s much closer to Naxos and a lovely little island. There are two ports on Amorgos — Katapola and Aegali. I stayed in Katapola and loved it but Aegali has better beaches. Read reviews & decide. Spend your 3 nights there, then ferry back to Naxos and ferry or fly back to Athens to complete your vacation.

Save Crete for another trip. It’s a wonderful island — we’re making our 5th visit this year — but it’s very large, further away, and worth more time than you have this trip.

And then save the Athens sightseeing for the end of the trip?

Yes, coming from the USA, it's always a better option to take a flight to an island upon arrival in Athens, provided, of course, that the island has an airport. Save Athens for the end of the trip.

Is there another island better recommended than Crete?

"Better" is a subjective notion; there are more than 150 islands worth visiting in Greece, each one different.

"Not touristy. purposely avoiding the popular islands."

Among these more than 150 islands, Crete and Naxos are in the top 10 most popular and touristy islands. (Crete is by far number 1)

Without knowing why you chose Crete, be aware that Crete is so large that you won't necessarily feel like you're on an island, and 3 nights is only 2 days, far from enough to discover Crete, which requires more than 10 days to be even partially explored.

I would agree with Charlene. Forget Crete, 3 nights is too short. Save those days to add to your stay on Naxos. You could also spend them on Amorgos + 1 night if you can avoid the first night in Athens.
Note, however, that Amorgos doesn't have an airport and it's about a 10-hour ferry ride back to Athens. This is the price you pay for "less touristy" islands. In the Cyclades, an island with an airport is allways very touristy.

Regarding the return trip to Athens, if you want to avoid a 10-hour ferry ride from Amorgos, a viable option would be to return to Naxos (by ferry) and then take a flight to Athens. Of course, this is only because you specifically said "Not touristy, purposely avoiding the popular islands" and you're sticking to that request.

Just in case:

https://amorgos.gr/

Another reason to have Athens at the back of your trip. You don't want to be stuck on an island due to any unforeseen circumstance like bad weather or a strike and therefore miss your flight home.

And another vote to change Crete for another destination. Crete is like a country on its own and 3 nights (which equals only 2 days) is way to short to experience Crete.

Agree with the others about Crete

I spent a fortnight about eight years ago on Naxos and did a trip report with photographs. You will see it has a small airport for smaller
planes to fly to Athens which may avoid a ferry journey. Forget prices as they are changing fast since the covid period of 2020.
I did not have a car so walked everywhere I could whilst my wife enjoyed the beach and then the swimming pool around our hotel.

You might find some of my walks towards the end interesting

https://www.tripadvisor.co.uk/ShowTopic-g189431-i1324-k11705901-Trip_report_for_Naxos_via_Mykonos_for_days_1_to_5-Naxos_Cyclades_South_Aegean.html

https://www.tripadvisor.co.uk/ShowTopic-g189431-i1324-k11708834-Trip_report_for_Naxos_via_Mykonos_for_days_6_to_10-Naxos_Cyclades_South_Aegean.html

https://www.tripadvisor.co.uk/ShowTopic-g189431-i1324-k11715100-Trip_report_for_Naxos_via_Mykonos_for_days_11_to_15-Naxos_Cyclades_South_Aegean.html

I can give you places on Crete but it just does not appeal to me like other places but we are all different

I am one of the dissenting votes to do Athens at the end. Arriving from the US ( especially West US) the journey is long and very tiring. The last thing my husband and I want to do is get on yet another plane even for a an hour flight and travel more. Coming from Seattle, and have made a dozen or so trips in the last 55 years, we always stay in Athens for three nights, get over jet lag, see the sights and then head either out to Crete or the Peloponnese for the remainder of the trip. We always come back to Athens mid after noon the day before our flight home ( usually it is a really early flight) and stay at the Sofitel. Expensive but a nice splurge. I want the parting memory of goat bells to be ringing in my ears when I leave Greece and not the sound of traffic and car horns.

A lot of factors are involved on going directly to your final destination upon arrival at the Athens Airport.

When is your flight/ferry going to the destination is the most important.

If it is scheduled before your arrival then it obvious you'll have to stay in Athens or very late departure after your arrival them it's better just to stay in Athens whether for a day or several days. Just depends on how late after your arrival. Do you really want to spend hours sitting around in an airport/port or spend the day in Athens then head out the next day.

Same is true for a ferry.

I've done both: go directly to the final destination or stay in Athens.

Worked well for me either way.

Most importantly you want to return to Athens at least 1 day before heading home just in case of any type of delays.

Trying to return to Athens on the day of your departure could be risky but some people take the risk and hope it works out.

If not you could end up paying a hefty price for another flight home.

My daughter and I went to Athens and Naxos last June as a high school graduation gift and we did 3 days in Athens, 4 days on Naxos, then a day and a half back in Athens. I had started booking hotels and flights before I read here that it's recommended to save Athens for last and I was worried that I had made a mistake, but it worked out really well for us. I was ready to be DONE with travelling by the time we got to Athens (we didn't have a direct flight), and we are city people so the hustle-bustle of Athens was not a big adjustment for us. It was nice to relax on Naxos with relatively cooler weather after the heat of sight-seeing in Athens. And my daughter wanted to buy some jewelry as a souvenir, she was able to check out prices at shops in Athens, then compare to prices on Naxos. She realized that for what she wanted, she could get a better deal in Athens so she was able to make that purchase when we got back there. Whatever you decide to do, definitely leave some buffer time before your flight home in case of flight/ferry delays or cancellations. Enjoy!

Note that if you plan a return ferry to Athens the day before your flight, and the ferry is canceled that day, there will be a high probability that taking a ferry the next day will also be too late to get your flight.

Since it is a question of giving personal cases, since the 90s that I started traveling in Greece, it has only happened twice to me to miss my return flight. The first time when I had planned the ferry back to Athens on the same day as the flight (beginner's mistake), the second time when I had planned a ferry the day before and the first ferry the next day arrived too late anyway to catch my flight.

There are as many experiences as there are travelers, no one holds the Truth, .

We travel to Greece from the west coast of Canada. We are really doing a transcontinental flight then a transatlantic flight. We arrive in Athens totally jet lagged. On our first trip we did Athens first. It is an intense experience trying to adapt to a foreign society when you brain is adapting slowly. Honestly it took us two days to get over jet lag and we were in no condition to appreciate Athens. Those were two lost days.
Now we always get to our first island immediately after arrival in Athens. Its way easier to get over jet lag on an island.
You need about 2 hours to catch a connecting flight to your island distention. Athens airport is easy to navigate and we have made connections in an hour but its best to plan for 2 hours.

Leaving Athens at the end of your visit has the bonus of being in Athens at least the day before your return flight. We were on a flight from Naxos to Athens that was delayed by 3 hours. At least half of the passengers missed their connecting flights.

By the way you are going to love Naxos.
Here is some images.
https://www.flickr.com/photos/stanbr54/albums/72177720329571437/