Take Route 14 East from Santiago towards Licey to Moca, go North on 21 out of Moca all the way to Sabaneta. Then East on 5 to Nagua and Samana.
21 is decent road, not a highway, but your most direct route.
If you are adventurous you can take 132 out of Moca through Salcedo, San Francisco, to Nagua.
No reason to go to Puerto Plata!
tambo'