Ten days in Greece

Adding either Naxos or Paros to your list would give you a nicely diverse island experience. Both are easily reached by ferry from Santorini and Athens. Both also have airports.

Mykonos which you can get to by direct ferry from Santorini that takes 2h and costs $67 per person. You can then fly non-stop to Athens from Mykonos. Naxos is closer, but Mykonos has more picturesque windmills.
Another idea is to take a direct, overnight ferry from Santorini to Rhodes, which people like more than Mykonos. You can rent two cabins and wake up in Rhodes, then fly non-stop to Athens from Rhodes.

Matt Barrett's website has a lot of info about Greece, including the islands. It may help you decide, and help you turn your choices into workable plans.

Unless you dislike big cities, Athens would seem like a good place for historical stuff. Nafplio would be a good base for the Peloponnesos. But don't try to "do everything" in just ten days.

Cameron -- if you will look down the topic list, you will see a thread "Greece in 10 Days" -- from another person having a short visit and not (so far) having done any homework. This question comes up every week -- so I'm going to save time & effort by just cutting my (detailed) answer to Kim and pasting it here -- just substituting June as the start date & deleting anything not relevant.
Here's the basic 10-day recommendation I have for newbies ... especially going in high season.
• LOGISTICS are all-important, and not over-scheduling. Remember it always takes longer to transfer from 1 place to another -- minimum of a half-day. So your max would be 2 short-stop islands, one longer, plus 2 days in Athens... and you'll need to fly mostly, just 1 ferru.

ARRIVAL DAY - June 27?. If u arrive late in day, stay overnight nearby & take early next AM to Santorini -- If you arrive before 10 am, why not try to fly mid-day or so to Santorini?? Going in to Athens & back out = waste of precious time!
DAY 2 (ISLAND #1 - SANTORINI. . I recommend staying on Caldera Side (best location - Firostephani). If you arrive early enough, you can walk down the "rimside walk," check out Fira Town, Enjoy sunset at resstaurant in Fira Town. (Do NOT attempt to see sunset in Oia, or dine there - the crowds can spoil the experience)
DAY 3 - Early AM (8 or 8:30) to Oia before tour crowds arrive, then vist rest of Island. Don't bother with beaches (black grit)
DAY4 (july 11)- Morning ferry to yr 2nd island choice -- NAXOS is ideal.. SO mch to do/see, not mobbed because no cruise ships or jumbo-jets for package tours. Hike, swim, drive thru mountains, visit ancient ruins eetc. its worth at least days. I recommend staying at Plaka Beach, using frequent local busses to explore port town. Rent a car 1-2 days.
DAY 5 & 6 -- Explore Naxos! It has Mountains beaches ruins, villages -- so much variety. And u don't have time for another isle.
DAY 7 - from NAXOS fly 10 AM to ATHENS, (45 mins); taxi to Plaka area flat-rate around €40. Stay in this hisstoric area, away from big streets, you'll walk everywhere. (Hotel Hera, Phillipos etc is very handy on S side of Acropolis. In late afternoon, tour crowds are gone from Acropolis, light is golden, photo-taking great.
DAY 8-9 Explore the wonders of Athens! Rick Steve website has great tours, also step-by-step FREE downloadable audio guide to Acropolis, Agora, AND the Famou Archeologiical Museum. These are terrific because they enable you to visit these landmarks yourself, not with a big tour crowd. Also, you can time it to avoid the crowds. Study his website borrow a stack of guides from Library ... Prepare Prepare -- it will enhance your experience in Athens AND islands.
DAY 10 - off to Airport! You cannot count Departure day as a "Greece day" -- so you'll have to return again (and again) ... there's always more to discover!

Ooops my mistake ... I left in one date (July 11) from the previous answer ... I trust you figured that out & were not confused. Sorry!

Peloponnese is an amazing place with more sites than you can handle with your available days after the islands. Just a few places to look for (google) Mycenae, Nafplio, Epidaurus, Olympia, Arcadia mountain villages, Sparta/Mystras, Mani, Monemvasia, and many more. It depends on what you are looking for ...
Great landscape, coastline, mountains, food, wine, historical sites newer and very old too.
You can explore the Peloponnese by yourself by renting a car or book tours with an agency to show you around.
You can get some ideas about what to visit from this private tour agency.
You can also do Hydra island.
And a word of advice; don't spend more than 1-2 nights in Athens, if you are planning to see the sites of the city.

Planning 2nd trip to Greece with my daughter-in-law and grandson who is an archeology nerd.

Try this website - www.davestravelpages.

You can get a fast ferry from Santorini to Mykonos. Dave talks about an evening tour of Delos which was reasonable as it includes boat ride and guide.

Delos is a must if you are into archeology at all. Main town is small and fun to wander around.

Depending on ferries to other islands/mainland you might only need 1 night in Mykonos. I'm planning on two and possibly renting a car.

Dave's website is easy to get around and had some good sight-seeing options.

MGS