How to spend 6 nights June,2015 between Athens, Mykonos and Santorini?

I think your plan sounds good, but you might consider 3 nights on Mykonos and 2 on Santorini. Just off the coast of Mykonos is the tiny, uninhabited island of Delos, full of ancient Greek ruins - a nice day trip by boat from Mykonos. The beaches on Mykonos are also a bit nicer than on Santorini. The order you do the islands doesn't matter much, as their are frequent flights between Athens and both islands. You might check the flight times from each island to Athens to see which has the best timing with your return flight. See www.skyscanner.com for options

2 islands and Athens is tight for 6 nights. Along with your comments and Rich's above, I would suggest the following:

If you have not booked your flights, consider paying a bit more and fly directly to one of the islands and do Athens last, or do Athens first and fly directly back from Santorini. I do not suggest just getting a separate budget airline ticket, since delays or tight connection may cause you to miss a flight. You likely will still go through Athens, just with a guarantee to get where you need to go.

As for 2 nights in Mykonos and three in Santorini and vice versa, that depends on the ferry between the two islands. If the ferry from Mykonos to Santorini leaves early in the morning, then do three nights there, if it leaves late in the day, then do two nights there and three in santorini, same logic if you hit Santorini first. Consider too your arrival on the first island and exit from the second, basically try to balance out the actual time on the islands. Arriving late on an island and leaving early after two nights leaves very little daylight on the island.

The way to be most time-efficient is NOT to have a night in athens, but immediately upon arrival, fly to your first island. Then do your Athens thing at the last. Going into central Athens twice is an unwise time-eater.

As for fllight booking, I must respectfully disagree with Paul. I have taken that same flight year after year (USAir nonstop from Philadelphia) and it is NEVER late. Even if it takes off an hour late from US, it has 9 or 10 hours to make up the time, and it always does. In June, getting thru passport control and customs (the latter nonexistent) and getting some Euros at an ATM takes 45 minutes ... and in June there are many many daily Aegean or Olympic flights to either Santorini or Mykonos. Therefore, this couple can very easily get a 12 noon flight with plenty of time to spare. And as for "a separate budget airline ticket" that mainly applies to European-based airlines flying from Europe. If u come from USA or Canada, its Aegean/Olympic, period. However, you still can save if you go to Aegean website and sign up for their "newsletter" (really just an e-mail alert). You can check these alerts for promotional fares to your destination ... June ones show up in winter == Jan or Feb. POUNCE, and you may get a flight for €39... cheaper than ferry.

We will be flying from Tel Aviv to Athens on June 17th. Should I plan to book flights on Aegan/Oylmpia to hop islands or are there other airlines we could use?

Thanks for all the suggestions. Can anyone recommend hotels or B&B's that are charming yet in a good location?

Aegan/Oylmpic are your only options from Athens for domestic flights to the islands.