I agree with the ATM. There are plenty of bank ATM's at the airport. When you get off the plane get 100 or so Euros. It is far easier than running to the bank and ordering Euros. If you do go to your local bank, call first and make sure they have foreign currency or you'll have to make two trips.
You have also been given good advice in notifying your bank about traveling and using your ATM/Debit card outside the U.S..
I do STRONGLY advise that you do get some Euros. Perhaps, certain tourist and port area shops will take U.S. dollars but if you are outside those areas U.S. dollars will not be easily accepted. Use your credit card for as many purchases as you can and I also suggest that it be a VISA card. The old commercials are true. "They don't take American Express". Amex is not accepted in as many places. If you use Discover then just leave it at home.
Have a great time and enjoy the beauty of Greece.