Having been to Greece myself many times, most recently 6 months ago on a 17-day 9 island trip, I can confirm you will be fine almost everywhere with any major credit card (MasterCard, Visa etc.)
I'm not sure if it's an option in the US, but here in the UK we have prepaid travel cards where you can load money onto the card and use it as you would any debit or credit card. Many of these are specifically aimed at travelling abroad so have no currency exchange fees. They are also more secure as you can only lose what you've loaded onto the card. If this isn't an option then just find a credit card provider who offers the best exchange rate for Euros and sign up.
Depending on your travel plans I would also budget perhaps €50 per day between you in cash (up to a maximum of €500) for your trip. Use cards whenever possible (meals, car hire, ferry tickets all usually accept card payment) and keep cash back for incidentals (taxis, drinks in bars, bus fares).
If you get near the end of your trip and find you have a surplus of cash, start using it more and aim to spend the last €20 at the airport before you fly home - it's rarely worth changing currency back as you'll get a much poorer rate than you paid for.
As the other answers have mentioned, when paying by card always opt to pay in Euro and let your card issuer handle the conversion.
Most importantly of all, have a great trip! Greece is a superb country and I'm sure you will love it.