The U.S. dollar is the American currency and the only one the is officially accepted anywhere in the country. If you arrive in the U.S. with British pounds or Euros or even Canadian or Australian dollars, you will need to get them exchanged. It is best to have your Rands exchanged before you get to the U.S. as it will be difficult to find a bank that will be willing to handle them except in very large cities.
Credit cards are widely accepted everywhere and you can use your Visa, MasterCard, American Express, Discover card and Diners Club cards at places that accept those cards even if the cards were issued in South Africa.
Keep in mind the current exchange rate. The rand has been faring poorly against the dollar for quite some time. To find out currency exchange rates, click here.