Can anyone shed some light on this itinerary

We made trips to Greece, two years in a row. The second time, in 2019, was just on Crete, and after 3 weeks we still could’ve gone to more places on the island. Hania (aka Chania) was our last stop, for several days. We flew from Denver to Crete, connecting thru London, and arrived in Iraklio (aka Heraklion) and departed from Hania (aka Chania). If Hania’s your one Crete destination, then Aegean Air and Sky Express both fly there from Athens.

Taking ferries between islands has been a popular way to connect them, although flying might be an option, too.

My guess is that getting home from Naxos will involve a connection in Athens, which is why many suggest staying in Athens towards the end of a Greece trip.

but we'd rather do the more touristy part first

Crete, Santorini and Naxos are as touristy as Athens. Santorini with around 15,000 inhabitants had more than 3 million visitors in 2023.

then settle into more relaxing and aquatic fun

Without mentioning that it takes more than 10 days to enjoy Crete. If the goal is to settle down and relax, it is not by visiting 3 islands in roughly a week that you will achieve it.
Each trip from one island to another takes roughly a day. So in your itinerary as it is, you will have 4 days of travel, or approximately 50% of your vacation time.

And how does one get from Naxos back to Boston?

If you don't want to swim :)) you will have to return to Athens by ferry or with a domestic flight, this is one of the reasons to save Athens for the end of your stay.

When I say "do the touristy things first", in Athens I mean the Archeological or educational stuff. For example, when we went to Italy we saw Rome and Florence and saw the historical aspects there, then proceeded to Amalfi and Capri for more sun and fun, if that makes sense. Would prefer to do the same in Greece.

The suggestion to do Athens last has to do with the logistics of getting from an island to Athens to get your flight home.

Can you book a flight from Naxos to home as a SINGLE ticket?

If not, you need to be in Athens the night before the Boston bound flight. That means your last full day is centered around moving to Athens, rather than doing fun stuff.

Doing the "heavy' tourist stuff first and having 'island time' at the end is not intrinsically bad, just a bit of a logistics issue of getting from the island to Athens for the homeward flight.

Consider spending most of your time in Crete, it’s a larger island packed full of everything you could want. Spend a few days in Heraklion to visit Knossos and the archaeological Museum. Then go to Phaestos, another great palace but without the reconstructions of Knossos. Stunning site and location without the crowds. On your way to Phaestos, stop at the Roman site of Gortys and wander through the olive groves to find ruins. Visit the south coast of the Island for sea and beach time. Visit Chania and stay at one of the smaller towns just outside like Kalives or Almyrida with nice beaches and swimming. Visit the island of Spinalonga near Agios Nikolaos, a Venetian Fortress with an interesting history. Hike one of Crete’s famous gorges. Enjoy Cretan food, Crete more or less invented the Mediterranean diet; and visit one of the oldest olive trees in the world. Then spend your last few days in Athens doing the main sites. To get anywhere in Greece you have to fly into and out of Athens, unless you go through somewhere like London or Frankfurt.

Too much time wasted traveling for what you want to do and not enough time for either island, especially Crete.

Crete is the largest of the Greek Islands and would take weeks if not more to fully experience everything it has to offer.

Santorini is the most touristed and expensive of the Greek Islands and should be thought through carefully to ensure you are aware of the crowds during you'll encounter.

Naxos is very nice and could possibly be combined with Crete but it's about a 6 hour ferry ride.

As mentioned why not stay in Crete your entire trip and settle in and explore one of Greece's nicest islands with something for everyone either touristy or non-touristy.

Also Athens should be saved for the end of your trip if possible. Three-to-four days would be sufficient to explore the city including touristy and non-touristy parts.

Fly back from Athens to Boston is your best option and that it's why many recommend Athens for the end of your trip to ensure you can get to the airport in case of any delays.

We were able to purchase tickets to Chania, Crete from US on one ticket through United. If you can do the same, you could go to Athens first, then Naxos, then Santorini, and finally Crete. .

While planning keep in mind that Crete is 160 miles long while Santorini is only 10 miles long!

If you visit Santorini first, you don't have to fly through Athens to get to Santorini from Boston. We live in Massachusetts, and we fly out of Logan Airport. When we visited Greece 2 years ago, we flew from Boston directly to Santorini with a layover in Zurich, all on one ticket. This way you don't have to worry about your luggage until you arrive in Santorini. You don't have to worry about how much time you need in Athens to get your luggage, find the next terminal, check in again, and go through security. Easy peasy.

We didn't visit Crete (visited Nafplion on the Peloponnese instead), but otherwise our itinerary was very similar to yours. This is what we did (to help you with logistics and transportation):
Fly direct to Santorini via Zurich
Blue Star Ferry from Santorini to Naxos - 2 hour trip
Fly from Naxos to Athens where we picked up our rental car for Nafplion
You would instead take a taxi to Athens.

I do agree with the people who suggest saving Athens for last. It does make the most sense logistically. Otherwise, you waste a night having to return to Athens the night before your departure. If you decide to do this, I assume there are hotels near the airport where you can stay your last night. It takes about one hour each way in/out of Athens. So that eats up time, too.

Thanks for all of the advice!

I have traveled enough to completely recognize the pitfalls of overstuffing a trip with too many stops. But that being said, there's no chance I am traveling to Greece without seeing Santorini and Naxos. And Crete for that matter. I don't anticipate ever returning to Greece, so we'll just make the best of making so many stops!

Greece has a way to captivate your heart and can call you back time and time again. After our first trip to Greece we were planning the second one on the flight back home to Canada.

Have returned 19 times since then.