When you are going away for just a week, the length of time it takes to get there makes a difference. The Dominican Republic has seven international airports, and at least two of them have regular flights to/from major U.S. hubs.
The driving distance between the Punta Cana airport and the area’s accommodations is short.
You can get flights from Europe at least via Madrid (MAD), Paris (CDG) and Munich (MUC). From the US, you can fly from New York, Ft. Lauderdale, Miami, Philadelphia, San Juan, Atlanta or Charlotte. Most European and Canadian cities have charter flight connections, which operate seasonally.
You will be charged USD10 for a tourist card. This can be purchased on arrival or in advance through the government’s web portal, which delivers the tourist cards via PDF download immediately. This must be paid in US dollars or euros. Local currency, sterling, or other currencies will not be accepted. A departure tax of USD20 cash is payable on most charter and some scheduled flights.
Taxi fares to nearby hotels are posted just outside the airports. From the airport to Santo Domingo (Ciudad Colonial) it’s about USD40.
At the airport, you can change your US dollars and euros in Dominican Pesos. Note that you may not be able to exchange back local money to US dollars and euros, so do it before leaving.
There is a ferry that travels between Mayagüez in Puerto Rico and San Juan in the Dominican Republic. The website says the journey takes 12 hours, leaves Puerto Rico on Mondays, Wednesdays and Fridays at 20:00, and arrives in the Dominican Republic at 08:00 the next morning. For prices and bookings, visit the Ferries Del Caribe English language page.