2 moderately active people want to spend 3 days after a guided land tour on an island, soaking up the culture. We'd love to walk/hike with great views, easy snorkeling/kayaking, maybe yoga, generally avoiding expensive, touristy areas. Luxury and a party scene are not what we want. While architecture and history are interesting, those are not the focus of this trip. This will likely be our only chance to experience a Greek island...what do you recommend? We will be arriving from Athens (via plane or ferry, TBD).
Since you are already late in making plans for Greek isles in summer (they have been discovered by mass tourism), if you need useful information, you need to be completely specific. What Days exactly will you have? What time of day will you arrive at (1) airport or (2) ferry port from your guided tour? Are you OK with accommodation that is not directly on the beach, but perhaps a few hundred yards away? Do you mean 3 full days (that would be 4 nights).... or on the 3rd day afternoon, would you need to get back to Athens, iln order to board your homebound plane the next morning?
Without these key facts, we could just randomly enthuse about quite a few islands, but that info would be useless if you try to find accommodation in High Season... all will be booked. We can help but not with guesswork.
I have always trotted out Folegandros for this answer. It gives visitors two aspects: a very picturesque hora (hike to Panagia church a must) plus a full-on agricultural hinterland--with more views. Throw in dramatic cliff scenery plus a public bus running down the spine of the isle and Folegandros has a lot to offer.
One gets there either by ferry from Athens OR instead hydrofoil from Santorini.
Good luck.
I am done. The end.
Reading your post, the only place I know that could ticks all your boxes and comes to mind is this one:
https://maps.app.goo.gl/ueEqeocqMjVWd9Qs5
Which is right next to this diving center, one of the best in Greece:
https://www.amorgos-diving.com/
There are plenty of others, but since you don't give any more specific information, as Janet said, we could recommend dozens of places you'll never go to anyway.
Yes, I realize we are late in planning- it is overwhelming. We can be ready to travel in the early morning on June 8 and will leave Athens at noon on June 11. From what I've read on here, we need to be in Athens on the night of June 10. While beachfront would be nice, we don't plan to spend much time at our lodging- we want to be out seeing the sights, etc.
One other question- does your recommendation change if we do not want to rent a car?