All things considered, it may be smartest to exchange your money for Euro notes at your home bank before you leave. Banks will often have the most reasonable exchange rates. Remember that some countries (such as Switzerland and the Czech Republic) don’t use the Euro.
Beware of using ATMs in Europe, as these are sometimes hard to find and often have shockingly high fees. The number of stores and restaurants that accept credit cards is fewer than in the U.S., so it pays to keep cash on hand when you can, but be sure to keep it secure and don’t be flashy with it.