You can bring some American dollars to exchange at the airport just to have a little in your pocket. Then use a debit card from your bank to withdraw more from an ATM. Don't use a credit card because interest rates will begin to acrue immediately. And the advice is that you should also bring enough American cash ($110 currently) to replace your passport at an American Embassy, in case it is lost or stolen. Otherwise you would have to change euros back into dollars.
My husband put our reserved dollars into a money belt he wears. Looks just like an ordinary belt. But in most countries, just carrying your money as usual is safe enough. Leave it in your hotel safe if you can.
We have a credit card from Capital One that charges no transaction fees (a fee to change euros into dollars). If you have one like this, bring it and try to pay with credit whenever you can. Saves trips to the ATM and there will be no fees at all. Not all places take credit cards, though.
Speaking of passports, scan and make a few copies of your passport, the page with the picture. Carry that instead of your actual passport, unless you are going to cross a border. Also scan and copy any credit cards you will be carrying and keep them somewhere other than your wallet. If your wallet is stolen you will have all the numbers right there when you call to report the loss.