We definitely recommend renting a car if you will be in Puerto Plata. There is so much to see and do on the north coast. You would be very limited by going by taxi. Check out our sponsor, National Car Rental at
http://www.dr1.com/national
They are one of the most reputable, if not the most, in the DR and after having recommended several clients their way, even family, we know they offer good service all the way.
For where to go... check out the left side bar at the opening page of our travel section at
http://dr1.com/travel/index.shtml
Check out the destinations marked as Puerto Plata, Sosua, Cabarete and Playa Grande. Lots of suggestions of what to do and see.