the only fee I pay is a 3% exchange fee, which is way less than paying an extra $5 per withdrawal and affords me the luxury of withdrawing an extra 20euros if I need a bit more cash.
Sorry Here There but paying 3% on an ATM withdrawal is very expensive. The banks, such as Bank of America, which charge a fixed fee, typically $5, plus a percentage are thieves and their clientèle should really find a bank which wants their business.
EU banks do not charge for ATM withdrawals. The exchange network, such as Maestro or Pulse, typically charges 1% of the transaction total as a currency conversion fee. Any other charges (foreign transaction fees) come directly from your local bank for no other reason than they want your money. Local banks do not provide any service specific to foreign ATM withdrawals.
I would always travel with some cash but it need not be in any denomination other than US dollars. It is best to use EU bank ATMs to obtain euros. Obtaining euros while in the USA is very expensive and not necessary.
Credit cards function similarly. However there is a huge difference in what they charge customers for international transactions. Capital One 360, USAA, and Andrews FCU, among others, offer credit cards which charge you the least for international transactions - typically 0% which means they refund the 1% currency conversion fee.
One point to keep in mind - never accept DCC or dynamic currency conversion. This is the credit card option you may be given to pay a bill in your home country currency. Always pay in the local currency, euros in this case, never pay in dollars if you are outside of the USA. There are two reasons:
1. the exchange rate offered is typically not the current mid market rate and is usually far less advantageous for you.
2. Visa and Mastercard changed their user agreements some years ago and even if your transaction is in dollars, you will pay any normal currency conversion or foreign transaction fees if the transaction is completed outside of USA.
Granted, many will find that these tips save them little in overall costs if they rarely travel outside of the USA but for others, the savings can really add up.