Yes, they do accept US Dollars or Credit Cards.
But if you want to buy a more expensive pieces, like jewels, it depends on the Credit Card, how much you can get off the listed price.
If you pay with American Express, the discount is lower than paying with Master or Visa.
But take enough small bills with you. When you will buy some souveniers, you can get problems with the change. Sometimes they tell you that they only give you the change in their currency.