I am trying to get a feel for the number of services that will accept a credit card. I know hotels, car hires, and many tourists shops do (especially if in a larger town). What about petrol stations, archeological sites, museums and restaurants? I use an ATM to take out cash, but we are heading out into the byways of Crete and I don't want to go hungry because I suddenly discover that no one takes plastic.
Your US credit card will not work in a petrol station because they require the "chip" card, while almost all US banks/etc have only the by-now oldfashioned "swipe" cards. Thus u must seek out manned petrol stations & pay cash. And in my experience, some of the nicest small family tavernas do not take credit cards -- because their prices already are so reasonable, they cannot afford the % fee that the CC companies charge.
For cash from the ATM, I trust that you already know to tell your banks AND credit card companies that you will be using CCs and ATM cards in Greece & give them the exact dates... otherwise as fraud protection, if they see activity from Greece they will freeze your accounts. For the ATM to your checking, also request a raise in the per-day withdrawal limit. Many banks put this at $250 or so, but will readily raise it to $500 or even $750. I hasten to say, this is not because you want or need to spend $500-750 per day!! No no -- it is so that you need go to the ATM infrequently. Also, since if you use an ATM on a Biggie Bank account (Chase, TD, Bank of America etc), they charge $5 per transaction + 3% of amount drawn ... so best to cut down on your ATM visits -- OR open an online account like Schwab or Capital One, or a credit-union account (as I have done), to avoid these fees.
Other tips: good to have an ATM card on a 2nd account, just in case (the "belt AND Suspenders" approach to travel). If u & spouse share an account, you EACH should have a card for it. Finally, its also prudent to use an ATM machine attached to a bank or in a bank lobby, during business hours, rather than at night or a free-standing machine. There may never be a problem (I have had none, in 11 greece trips) but why not be prudent, for peace of mind?
Finally, credit card usage may be advisable or not, depending on how "deluxe" your card is. At home, you can use yur card everywhere -- gas, groceries, ice-cream stores, even shoe repair! -- and if you pay off the bill at the end of the month, NO cost whatever to you, for the convenience of "plastic". Different story overseas! If yours is a "plain vanilla" no-fee card on one of the biggie banks, you will find it levies a 3% fee on anything you charge. Thus a $500 hotel bill (€385) will have $15 tacked on. Why?? Because They Can ... no other reason. Alternatives exist: If you have one of those "super-sapphire" or VIP cards, it may charge you NOTHING for its use. Again, if you have an online credit-union card, they may have no-fee or a small one. If you have a bit of time before your trip, this is worth considering.
Museums and sites will almost all take cards. Gas stations mostly will, but you may have a harder time with those if it is not a chip & PIN card. Restaurants are a crap shoot. Some do, some don't. Small, local restaurants are less likely to take cards. And an ATM is never far away.
Every trip to Europe, we find we can use our Visa card more and more. As long as the petrol station is open, there will be an attendant who can swipe a non-chip card and ring up the transaction. We still withdraw cash at ATM's, for taxis (although some take plastic), and generally small transactions. Also, many B&B's, apartments, and hotels either request cash, or insist on it, so we've often needed to withdraw cash with our lodging in mind.
Haven't been to Crete, so your results may differ from ours elsewhere in Europe.
Thank you everyone. The I info about gas stations was very helpful. This is my first trip without a bus tour, so there were some things I needed to get straight from my previous European odysseys.