Phone in Greece for 2 weeks in September

I switched over to TMobile for their $50 monthly all the Megabite you can use/$.20 per minute voice plan--worldwide with no monthly contract. If you're not on a monthly contract with ATT, try'em for the time you're gone. You can always switch back upon returning home.
The phone works just like it does here, including people calling you @ 3:00 a.m. thinking you're home.
When we travel, most communications are done via WiFi on a 1 pound Chromebook from hotels and restaurants when in port. Ships' WiFi is too expensive.
You can easily find WIFi on Mykonos in restaurants along the waterfront and in hotels.

I second the TMobile recommendation. It couldn't be easier - you show up, turn on your phone and it works. Data and text are free and unlimited. Calls are at 20 cents per minute, unless you call over wi-fi - and then it's free. Stop by one of their stores and you'll see - it's just great!

"Data and text are free and unlimited. "

Data may be unlimited but I believe the "free" T-Mobile data is at 2G speeds. You can minimize text costs by using something like Viber where Wi-Fi is available. Viber can also be used on 3G / LTE (which will normally incur charges) but that option can be switched "off" in the "Use Cellular For" menus.

Your best bet would be to pick up a 'PrePaid' or 'Pay as you go' SIM card from one of the major carriers in Greece (Vodafone is one carrier). Each carrier typically has different plans available, so ask for one that has the best international rates. I can't tell you exactly what the costs will be in Greece, but to give you an example of the potential savings, I obtained a SIM card in the UK which allows me to call the USA for .02 per minute and it also provides a good level of 'data'. You 'top up' you SIM initially with say, 15-20 Euros or whatever amount you anticipate using, and if your balance runs low, you can Top-up anytime on the phone.