Is it cheaper to buy Euros in the US before you leave for Europe or use the ATMs for cash and your Capital One credit card when you get there?
ATM is your best option as is credit cards for purchases. Worst is using credit card for ATM withdraws. Only reason to buy Euro's beforehand is the convenience of not needing to stand in line at the ATM machine at the airport. (Which could be a long line) But the exchange rate is not as good as the ATM route.
Gordon - please check around the board some - there are several threads on this topic (which is quite common) and most have lengthy debates...
This might not apply in all countries, but in my experience in German speaking countries, the really economical accommodations only accept cash. So, by insisting on using a credit card, you are probably limiting yourself to more expensive places. Other than that, I agree with Ed. Especially, take a few Euro with you to Europe, if only for piece of mind. And, if you think you will ever return, don't cash all your Euro in when you leave, bring a hundred or so back with you to start the next trip.
I have never found it cheaper to get Euros here in the U.S. before your trip (and I once worked for a national bank). Anytime you exchange you will pay a fee/discount that is significantly higher than getting cash from an ATM, even more than the banks that charge outrageous transaction fees on your withdrawals. I prefer to bring my debit card for cash plus some U.S. cash to exchange in an emergency. If I never use my emergency cash, I don't pay the cost of exchanging it into Euros (and possibly back into dollars). I haven't had any trouble finding an ATM in an airport on arrival, just make sure you avoid the exchange machines that masquerade as ATMs. I have had some trouble at/around ferry ports so might suggest using the exchange on the ferry for some starting cash.