Rick Steves' book is excellent on Athens, and good on the Peloponnese major highlights (not the minor ones), but don't count on him for info about Islands... his tours cover none at all, or just an overnight at Hydra, which he constantly promotes, although it has almost no beaches handy for day visitors (y ou have to jump & swim off rocks). For some reason, his organization doesn't seem fond of Greek Isles tho they are beloved the world over, and he seems to like Turkey better than Greece (I Have read too much history about what Turkey did in Greece and To greece over centuries, to be interested in Turkey visits)
EarlyJune is a great time to appreciate Greek island(s), if you plan an efficient Itinerary. You have only 8 1/2 days (you can only count day #1 if you arrive before 11 am, and can't coun Day #10 - departure day - at all). My suggestion:
(1) -ARRIVAL - Book an airline that is nonstop from N America to AThens -- these are the only ones that arrive in the AM -- from 9 - 11:30 or so -- and are consistently on time. This summer, European connections have been chaotic, full of delays and cancellations, and who knows when it will sort out?? You have plenty of time to find good flights from Missouri to the airports providing nonstops - NY, PHL, NEwark, Atlanta, Toronto/Montreal are few. If u have objectors who want to connect in Euroope so they can use their precious "travel points" kick them out of the group.
(2) ISLAND CHOICE - allow 2-hr layover time in Athens, &connect with domestic flight to ONE island -- I highly recommend Naxos. Largest greenest ISle in the Cyclades, fascinating port town, a string of wonderful beaches not crowded in June, great bus network, dramatic internatl landscapes -- NOT overwhelmed by mass tourism (because cruise ships can't dock, airport to small for big jets). Naxos has been "discovered" but is not yet "spoiled"... enjoy it now! NAxos & Paros are 2 of the only isles offering dedicated excursion boats... so your Santorini Die-Hards can get their look-see, ditto Mykonos-Delos. THere are also delightful day trips to local small "beach islands". You can rent car(s) one day to zoom around the island, or take one of the rewarding small-bus day tours. Naxos offers an opportunity to relax AND discover... it's still a pretty authentic Greece experience. Dining is a delicious time, with many tavernas now specializing in all-Naxian products
(3) BACK to MAINLAND - Spend 5 1/2 days on Naxos, and Fly back to ATH airport either the evening of day #6 or early AM on Day #7. Book "Welcome Pick-Up" or "City Cab" car service to transfer from Airport to a Central Athens hotel or Apt. Since there will be 5-6 of you, you'd get 2 standard (Mercedes) vehicles -- each will charge the legal "flat fee" from airport. You can also get a 6-8 psger mini-van, but no savings, and perhaps a tight squeeze for luggage.
(4) DO ATHENS LAST - on an isle, you've reinvigorated, & learned "how Greece works" -- thus ready for efficient big-city sight-seeing. In 3 days u can cover Major Landmarks, & also follow personal enthusiasms (Lallounis Jewelry Museum? Museum of Children's Art? the Melina Mercouri Foundation?) The list is endless...
(5) FINAL TIPS - In Athens, choose rooms walkable to major sites. THis link - https://tinyurl.com/heq6edp - is a booking dot com "filter" that tells distance of each place from Acropolis - stay within 1 mile. BTW, Booking dot com now also lists pvt apartments in VERY convenient locations, at rates better than adjacent hotels. HOMEBOUND FLIGHTS - try for a departure no earlier than 10 AM -- trip to Airport is 1 hr, you must be in line 2 hrs before take-off ... And if you have to leave hotel before 7 am, it could put a serious crimp in y our last-night dinner celebration!