For a trip to Punta Cana, a combination of both is the most effective strategy. Major all-inclusive resorts, high-end restaurants, and large shopping malls readily accept major credit cards (Visa and Mastercard are most common), and using a card with no foreign transaction fees is usually the safest way to handle large expenses. However, you will definitely need cash for tipping staff (bartenders, maids, and tour guides), buying souvenirs at local markets, or paying for taxis, as many small vendors do not have card terminals. While US Dollars are widely accepted and often preferred in tourist areas, you will often get a better exchange rate if you pay in the local currency, the Dominican Peso (DOP). It is wise to carry small denominations of USD for tips but use Pesos for local purchases to avoid the "tourist markup" that occurs when vendors set their own unofficial exchange rates.