Dianne -- First of all, it's key to know, is this 10 full days on the ground? Don't count arrival & departure day... and u should be back in Athens area the night BEFORE your homebound flight. Now, to your destinations:
99% of the time, first-timers from USA only know about Mykonos & Santorini; I can only think it's because they haven't yet looked at a good guidebook, and tours/cruise lines unrelentingly promote those 2 islands; lovely but over-hyped and the costliest places in Greece. From May thru early Oct, midweek sees 2-4 huge cruise liners docking in each, so thousands of cruisers in main towns. Please do broaden your view. Thumbnail Advice -- Go in September -- October, even these 2 isles have a "closing down" feeling.
SANT: book room with caldera View (Oia, Firostephani abound it hotels); beaches r on other side of isle, not notable (black volcanic grit/pebbles). Main activities: Akrotiri archeological dig, dining, shopping. If u stay in Firostephani, u can walk to Fira (town) where in Fall there's more nightlife & more restaurants in fall. I say 3 days enough; honeymooners stay longer.
MYKONOS: also many hi-end shops. Lovely mazey port-town, lined with luxe shops (Hermes, Cartier, Calvin etc). Sandy beaches (windy in fall); good hi-end restaurants. Nightlife active longer than other isles. In Fall, Myk-Vets advise, stay in town, bus to beaches, not vice versa. Activities: Delos (the holy isle), swims, shopping. I say 3 days is plenty, but that's just me.
ISLAND #3: Right between the 2 - NAXOS, a 2+ hr enjoyable ride from Santorini on deck of modern large Blue Star Ferry 3:15 - 5:30. Isle has major year-round population, so port town always lively; it's also much more interesting not so focussed on Crui$$e crowds (no large ships can dock here, no jumbo jets). You can have balcony on St. George beach adjacent to town for a fraction of Santo/Myk rates ... array of friendly tavernas w. sea view, serving authentic Greek fare & fresh produce from Naxos farms. For beach lovers, there's 12 miles of golden-sand beach in a row, to stroll .. Excellent bus system, or u can rent a car for a day (30€) to zip around entire island. History galore! (ancient ruins, statues in orchards, castle atop town). My friend "Stanbr" has a photo album I love, of Naxos highlights: http://www.flickr.com/photos/stanbr54/sets/72157634605629689/ There are daily ferries to Mykonos (NOTE: choose car-carrying catamaran over plain catamaran; larger, more stable ride). From mykonos, ferry or flight back to Mainland. BTW: Do you plan ANY time in Athens? Or have you already been there?