Carnival Cruise Line has a stop in Amber Cove, Puerta Plata, I would highly recommend taking a Carnival excursion or hang out at the port at the Amber Cove Aquatic Park. This was very nice and only charge was for food and drinks and if you wanted to use the Zip line it was 20$ for the day.
If you wanted to take a taxicab to any local beach, prepare to pay a fortune each way!! Sad for the Dominican people, many cruisers stayed at the port!!!