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!