Greek islands Itinerary/Flight/Ferry questions with young adults

I would fly Athens to Santorini and then ferry to Naxos, and then fly back to Athens. I would eliminate Mykonos. To me, Mykonos and Santorini have more uncommon and naxos adds some variability (Naxos and Santorini are different experiences). That said, if you prefer Mykonos from what you've read, choose it. But dont travel between Naxos and Mykonos with those 3 days. That will take up too much time. Naxos has rocks to jump from, and snorkeling in caves, and other outings (hikes to beautiful churches, villages. The center of the island is a mountain). I imagine Mykonos has similar? As for ferries, Ive taken high-speed and regular and the difference want huge. You'd be fine with Blue Star.

I pretty much agree with Jessica about Mykonos.
The main activity in Mykonos in the summer is partying.

If you are looking for "beaches, scenery, snorkeling, hiking, historical sites, great food, etc". You'll find that in Naxos.
In addition if you only have 6 nights after Santorini, do not waste your vacation in the islands by traveling every 2 days

"Jumping off rocks" would rather be the specialty of Milos island, but that will be for next time...

Since you arrive quite early at Athens airport, take a flight to Santorini with Olympic/aegean or Sky Express.
From Santorini you will have two Blue Star per day to go to Naxos (the Blue Star Patmos in the morning and the Blue Star Delos in the afternoon). The crossing takes less than 2h30. This should be fine for people with seasick.

In Naxos if you are not too far from Naxos Town, the capital where the ferries arrive and depart, the kids can go out in the evening and will certainly improve their practice of Greek with the bartenders :)

Between Naxos and Athens, take the same Blue Star ferries as between Santorini and Naxos (the journey will be a little longer - between 5 and 6 hours).

They arrive at the port of Piraeus. All you will have to do is take the metro to reach your accommodation in Athens.

Thanks to both of you for feedback and now leaning towards Naxos. What about flying from Naxos to Athens over the Ferry to maximize time? Also, if some family members are adamant about seeing Mykonos, would it be crazy to day trip (as in a waste of time) to Mykonos? Thanks!

There used to be a day excursion from Naxos to Delos an great theological site, then goes to Mykonos for three hours before returning to Naxos.

I believe they were suspended for the past 2 years but are probably going to sail this season.
Its a good way to experience Mykonos without having to pay the exorbitant prices to stay there.

Check with any travel agent when you arrive in Naxos for information and prices.

For the ferry from Santorini to Naxos the blue star certainly gives you a long experience with a sea view of the caldera we normally choose to take the much faster and more expensive Seajets because it got us to Naxos sooner. It takes a different route through the caldera but I timed it on out last trip and I had a great view for 14 minutes.

Yes we always fly back to Athens from Naxos. There are two or three flights a day from Olympic and from Sky express. We always want o get to our next adventure the fastest way possible because time saved may actually be your most precious commodity on a short trip to Greece.

For fun here are images of Naxos.
Naxos town https://www.flickr.com/photos/stanbr54/albums/72157632094558042
Trip around Naxos https://www.flickr.com/photos/stanbr54/albums/72157634605629689
Naxos sunsets https://www.flickr.com/photos/stanbr54/albums/72157700728046481

You have very little time so do not try to divide 3 night between Mykonos and Naxos. I would pick Naxos over Mykonos. Mykonos is a party island in high season and not somewhere I would want to go with my young adult children. When we took ours in 2018, we flew first to Santorini and ferried to Naxos. We then flew back to Athens. That worked well. There are more flights to Santorini than Naxos so easier to do on day of arrival. Santorini is mostly about gorgeous views which are a nice antidote to jet lag. Everyone also speak English which makes for a soft landing in Greece.
As beautiful as Santorini is, we liked Naxos more. It is less crowded, has great variety of landscapes, and is more authentically Greek.
We flew from Naxos to Athens to save time. We took the early flight at 8:30 am I think. The airport is tiny and an experience in itself.. I would do that and also have transportation meet you. You have so little time that you need to buy yourself time however you can.
There was subway (which we planned to take) strike when we arrived and taxi line was forever. We took a bus which was our best choice but having transportation arranged would have been better.