Paying in dollars
Your best bet when traveling outside the country is to get a credit card with no foreign transaction fees. The credit card issuer offers a better exchange rate than the booth in the airport, as well as protection against fraudulent charges. Beware of shops that offer to process transactions in U.S. dollars. This "convenience" often comes with inflated prices.
You will probably still need some cash abroad. Use your debit card upon arrival at the airport ATMs managed by local banks. These are relatively free of fraud, and nearby representatives can exchange high denominations for smaller bills. Some U.S. banks even have agreements with foreign institutions and will refund ATM fees. Talk to your banker to learn more before leaving home.