Best way to spend 10 nights in Greece- Hoping to enjoy time in Santorini and Mykonos

I don't know where you "heard" that but sorry, one night isn't nearly enough time to explore Athens. Two full days is the least amount of time I'd recommend, three days is better. Also, if you only have a total of 10 nights in the country you actually have less time at your disposal than you think, since your arrival day is mostly wasted getting acclimated to your first destination (and don't forget jet lag), plus you have to return to Athens for your flight home. This should NEVER be attempted on the same day as your flight back home, just in case there's a problem returning to the mainland caused by mechanical failure or extreme weather. The best plan is for you to fly out to either Santorini or Mykonos when you first arrive at the Athens Airport, ferry between islands, then fly back to Athens for your last days so you aren't backtracking. This gives you those extra days to get to the mainland if something goes wrong. With your interests in mind I'd say Mykonos and Santorini are right up your alley.

We took the RS Greece Tour in 2014 and used the Lonely Planet Greece Guide Book for our stay outside of the tour. If you do not already have it, I would suggest you get it as it was certainly helpful for us. Also, you might want to check out the RS Greece Tour to see its itinerary. We spent a total of a week in Athens and feel we saw everything we wanted to see.

Our normal routine is to fly to Athens for two nights, then either ferry or fly to an island(s) then return to Athens for at least 1 night to make sure we are not stressed to have to fly the same day we return to Athens. Too many things can go wrong to fly/ferry from an island then try to make connections for your flight.

10 nights seems like a lot but you are splitting that time between three destination. I would recommend Athens then one island to really take the time to experience what you are seeing.

Mykonos and Santorini are two of the most popular and heavily touristed islands in Greece. Some people love them others don't bother going to.

If you want crowds, nightlife, high prices then Mykonos/Santorini is for you.

If you want culture, history, fair prices, more locals than tourists and a more "real" Greek experience then islands like Sifnos, Milos, Naxos, Amorgos, Skyros, Lemnos, Thassos, Astypalea and a number of other islands would be best.

All depends on what you want for a Greek Island experience.

I would skip Santorini , don't know about Mykonos , but Santorini is very congested , overpriced , & waaaaayyy over touristed .
You will spend most of your time struggling with the hoards of people in the narrow alleys .
My suggestion for only 10 nights would be to rent a car & tour the peleponese. You will get the same fantastic views minus the crowds , & at half the cost.

Thank you, everyone for the very helpful insights and suggestions :-)