Take some time to research money and the exchange rate where you are going. Even if the country takes the American dollar, you should take care to familiarize yourself with the local currency. Local Vendors who take the USD will most likely not give you the best exchange rate, thus negating any sweet bargaining you may have done. If you have the opportunity to use your ATM card, generally this will give you the best and most current exchange rate. Local Banks are also a resource for exchanging money.
If you do use US currency, be sure to carry crisp new bills. Most places will not accept worn, tattered or ripped money. Be familiar with the denominations of the local currency. Larger currency is not always a bad thing. For instance in China, a 100 Yuan bill is roughly $15 so you should carry them like you may carry 20s.