Currency in Greece and Turkey

My husband and I are taking the Treasures of the Aegean in a few weeks and I'm wondering about how to handle the local currencies. I usually try to bring a little local currency to start the trip and then get more as needed from ATMs. I've not heard about any difficulties in Turkey but what about with the current situation in Greece. Is it possible to get Euros from the ATMs in Greece or should we bring all that we think we're going to need? Also, how acceptable is it to use US dollars in either country?
Any help would be greatly appreciated.
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