Family trip - 10 adults

You will have trouble in Greece finding a house that fits 10 people. We had 6 people and rented houses in santorini, nafplio, and Athens. The house in nafplio was unusually big-it had six bedrooms. The other two had 3.

The larger houses on Naxos were not well located as they were built for tourists after the coastal areas had been developed. We opted to stay in one hotel there. We did rent the penthouse suite which had a roof top deck for gathering.

Santorini is very touristy. Naxos is not.

Because 10 people and only one week is so logistically challenging, I would start with flights.
Could you all fly to one of the islands with an airport to avoid having to transfer to ferries? Try Chania and Heraklion on Crete for example. Here is a webpage listing other airports on islands:
https://thepointsguy.com/2015/03/flying-direct-to-greek-islands/

When are you travelling? Most Greek islands that have airports are busy in the summer months. The quieter islands that don’t have airports obviously take longer to reach, necessitating a ferry ride.

Do you want historical sights or just beach time?

Greece has hundreds of islands. Islands that are less touristy than say Santorini, that I have visited include Lefkas, Paxos, Antipaxos, Kastos, Ithaca, Alonnisos and Kefalonia (Fiskardo town is very touristy). I have rented a small boat on Lefkas for a day to head over to nearby Meganissi.

Crete is better if you want more history. There are also some fantastic parts of the mainland. The Pelion is stunning.

You may struggle with a single property for 10 people. Look at Booking.com, Trip Advisor rentals and VRBO.

vrbo.com is actually a very good source for this sort of situation. I randomly chose a mid-May stay for 10 people on Paros (has an airport), where there is lots to do and some great beaches. The very first property that came up was a 5-BR/3-BA villa with a private pool for US $511/night: https://www.vrbo.com/6939336ha

This is obviously a beautiful house. One thing you need to think about is how your family travels together. When we went to Greece we did not want to be in a place where we would have to drive to do anything and that people could not go off and do things on their own. For example, when we arrived in Oia, Santorini my 21 and 25 year old sons dropped their luggage and went off to explore. The rest of us moved much more slowly-my husband even taking a nap. Villas like these are great if you want to spend significant time enjoying the rental and your group is easy to corral for day trips.

You have a horrendous task ahead if the responsibility is on your shoulders! I have counseled several other family groups like yours -- and it is like herding cats! (One important thing to remember -- if you & husband are footing a large part of the bill, you need to act like it; don't let the other 6 adults nitpick.) As others said -- when you want really useful help, you need to share more, i.e.,
• WHEN? July/ August are MOST crowded, hottest, most expensive. I strongly advise mid-June if possible.
• WHERE FROM? If some from West Coast = longest trek, most exhausting. Affects options for first-day travel
• HOW LONG? does "1 week" mean 7 days IN Greece? Or does it have to include the FULL day+ TO greece (12-15 travel, 7-10 hrs clock-time loss), plus the FULL day to return. Unless you have 7 days IN greece, I suggest you look for something closer.
... if you DO have 7 days there, here are my thoughts:

STRATEGY -- Since you have such a mob-scene, best plan is to get you All to ATHENS roughly the same day, and then take a domestic flight to your ONE destination. You will want to come back the night before your return flight(s), just to be safe. Also, wise to choose place where sights/activities are walkable or local transit easy, to avoid massive car-hires & constant driving.

GREAT IDEA - 2 earlier contributors beat me to it -- CRETE is a fab solution, especially WEST Crete, near CHANIA. The Old Town is stunning, the area is FULL of ancient history, and if you choose right, you can be on a gorgeous local beach a couple miles outside of Chania, served by a frequent local bus. I steered a family here -- GOLDEN SANDS -- https://www.goldensands.gr -- and they reportedly had a great time! Relatives were able to sightsee independently or together, and rent cars just for part of the time, for group outings. This online agency page http://www.travel-to-crete.com/hotels/chrissiakti/goldensand/ actually describes it better. Best part is, they have apts/studios of various sizes, so you all can be together yet not be lining up for a bathroom!

BEGINNINGS & END -- If you all arrive at different times in Athens, from noon to late day. you probably couldn't all coordinate getting on the same domestic flight that day. So... Only 20 min ride from airport (on FREE shuttle bus) is a modest-price hotel right on a beach - http://www.hotelavra.gr -- so early arrivals can have a swim & start their holiday while awaiting the rest. Then ALL can shuttle back to Airport early AM to catch the FIRST domestic flight to CHania Crete (also the lowest-price!). At end of your trip, you could fly back to airport ... OR there's an overnight ferry that leaves Chania 9 pm, arrives @ Pireaus (the Athens port) about 7 am -- actually not cheaper than flight (BUT if u take cabins, the fare is in effect your hotel room as well).

Wonderful responses and many, many thanks. You've all given me such good advice and considerations to work through. Our "group of 10" will be together for Christmas this year and one day will be devoted to planning this adventure. Dates are very much up in zither air.
To answer a couple questions, the entire trip for most of the family will be limited to 7 days due to work and school. We won't go in the summer. One daughter and hubby live in Switzerland, second daughter, hubby and grandkids live in Wisconsin & son and partner live in SC.
I like the VBRO idea as we've used their services in states. We have used Airbnb extensively in Europe. I hope some or all of you will reply my post after the holidays. Again, thank you for taking time to respond.

Good luck vicky. And you still did not answer my question of what does " 7 days" mean... does it mean 7 days IN Greece? Is that AFTER you subtract the travel time -- outbound 18-22 hours (when you put in the 7 hrs clock-time change), and 1 full day homeward bound. Unless this is 7 days in addition to travel days, Do Not Go to Greece. Save it for another time.

The best time to visit Greece is in June and September. You will get the best service everywhere. Greece has so beautiful islands and each island has something special.
If you never been to Athens, you can spend 3 days in Athens and the rest on the islands.
In Athens, you can't miss the Acropolis, Syntagma square and Plaka. From Athens, you can also experience a day trip with a sailing boat to moni,aegina and agistri. you have a swim stop on one of the uninhabited island which has very clear water, is perfect for swimming.
One of my favorite destinations is Sivota, Milos and Santorini.
Santorini doesn't have a very nice beach and water but the village of Oia with its whitewashed houses, blue shutters, sunset is one of the most photographed places in Greece.Is easy to get by Ferry from Piraeus port.

I would suggest that contributors hold off on any more suggestions until when/if Vicki comes back with more information ... we still haven't heard WHEN this proposed trip would take place, or whether the 7 days also includes travel to/from Greece (in which case I advised against Greece as a destination). There's no point in further guesswork and effort by helpers, without key facts.