Cyclades Islands- which to choose?

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?

Considering your dates, I would recommend against heading to an island. If you go on the 8, it’s unlikely you’ll arrive before noon at the earliest. And it’s crucial to plan on returning to the mainland at least a day prior to your flight, which pushes your return to the 10 at the latest.

So, you’d only have the afternoon of the 8 and the whole day on the 9 for your island stay. That’s really not enough time, even if you didn’t have planned any activities. In your situation, it just doesn’t seem feasible.

I appreciate your thoughts on this. Is there a coastal town on the mainland that you'd recommend instead that we should explore? Maybe minus the snorkeling/kayaking part.

I must note that it's frustrating when inquirers hope for very specific advice, while being very UNspecific about the dates involved. Is there a problem with sharing?? Our advice can differ drastically, depending on whether your "free dates" are in May, or late July-Early August! And even depending on what day of the week this period starts. Examples:

• What about a very accessible Island, Close to mainland, but ferries are not dailly? IF we knew dates, we could know if such a place might work (KEA is perfect example)
• What about other islands perfect for 2 days, and is only an hour from ferry pier, very enjoyable in May-Early June or Sept, during WEEK days -- but can be overwhelmed on Weekends by Athenian crowds (such as Aegina /Agistri).

If you'd given dates and either of above would be workable, I'd give full info, but if you make us guess, maybe not.

I did give dates in the reply. We are done with our land tour in Athens on the evening of June 7. We depart Athens on June 11. Essentially we have all day June 8, 9, and most of June 10 free, planning as many have suggested to return to Athens on the afternoon of June 10 to fly out on the 11th. Sorry if that wasn't clear.

I apologize for hasty re-reading & missing your additions. this does mean that you could check into either Aegina or Angistri (sometimes spelled Agistri)

AEGINA -- The night before, go to any ticket agency by your hotel and check timetable for conventional Open-deck ferries (avoid the closed-cabin hydrofoils) you can easily get to Piraeus in 30 mins on either the Green lline or Blue line Metro... or a taxi costing about €18-22. Here's a great phto-journal of a day-trip to Aegina -- http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/
it shows the island highlights and Ag Marina beach, a place to book a room if you want swims -- dont know about kayaks or snorkeling.

The port town is not all that touristy, Aegina is populated year-round by Greeks who commute datily to Athens for work. It's fun to browse back lanes for local grocery shops, home decor etc for a glimpse of Greek daily life.
Bus schedules sparse but there now are also electric bikes, so car rental not as necessary.

ANGISTRI -- very small, and you get around on bikes, so may be perfect for your 2-day stay. I know one easy way to get there is thadt open-deck to Aegina, than catch a 20-min fast boat to Angistri -- ask the travel agency for other options ... direct ferry to Angistri is closed in no view. Here's a 2025 TA thread on Angistri connection -- https://www.tripadvisor.com/ShowTopic-g189491-i2230-k15405783-Agistri_connections_ferries_to_which_other_islands-
SaronicGulfIslands_Attica.html
On Agisri, one place thats' beenaround a long time, https://www.rosyslittlevillage.com has good reviews, no beach essenitally steps down right into the sea. However the tiny port has a lovely beach running to one side, with tavernas and several nice hotels.. Another beach right next to it called Laza ... those are where I'd look.

I apologize for overlooking your addition on actual dates ... since theyre June weekdays, that's good for both Aegina and Angistri (often spelled Agistri).

The night of 7th just go to ticket agency by your hotel (they are everywhere) and ckeck timetables for conventional open-deck ferry to Aegina (avoid hydrofoils, closed-in). You can easily leave your big bags in your Ath Hotel storage & just tag small bags for a 2-nighter. Taxi to Pireaus is about €20+ or take Green line or Blue line Metro there in 30 mins.

AEGINA -- Here's a great photo-sequence of daytrip, a one-hour "mini-cruise" including ferry deck views. -http://www.flickr.com/photos/36264706@N03/sets/72157621604646139/detail/ it shows all highlights plus beach at Ag. Marina; that's where to book room if you want swims, don't know about kayaking. Snorkeling not too fruitful in Greece.
Port town isn't over-touristy; island lived-in year-round by Greeks who commute daily to jobs in Athens. Fun to browse towns back lanes for Groceries, home decor shops for glimpse of Greek daily life. BUs schedule limited, but they now have electric bikes for rent, as well as cars.

ANGISTR1 -- may be even more your style with only 2+ days... tiny, only thing to do is beach, stroll, bike though woods. Best location for rooms -- the nice beach on one side of tiny pier, and another next to it, calle Laza beach. Plenty of tavernas and cafes. TO have that nice open-deck transit, sail to Aegina & connect with 20-minute fast boat to Angistri. There may be closed-in fast-ferry driect to Angistri from PIreaus -- ask at your Athens ticket agency.