Try to pick up a map at a large pharmacy or supermarket on the way.
Your points will be Samana, Sanchez, La Majagua, Nagua, Cabrera, Abreu, Playa Grande, Rio San Juan, Gaspar Hernandez, Sabaneta de Yasica, Cabarete.
There are some sort of signs for these places. Best is to go asking as you get to each town so you make sure you are on track. As pointed out, you want to make sure you take the right direction leaving Nagua so you head north and not west (that would take you to San Francisco de Macoris). When you get to Nagua, ask for directions to go to Puerto Plata and people will head you in the right direction. For most of the trip, as Hillbilly points out, you will be seeing coastline.