Six days is not too much time. I recommend you stick to the north coastline. You do not tell where your hotel is located. Regardless, Puerto Plata vacations can be split with time for Cofresi (Ocean World Park), Damajagua-Imbert (take note this may leave you exhausted for the day), Playa Dorada, Sosua, Cabarete and Playa Grande. For the attractions of these places, see
http://www.dr1.com/travel/index.shtml and then the sidebar to the left with links for what to do in these places. Nightlife in Cabarete is great. Taxi is recommended. You could probably do Sosua beach during the day, and then get to Cabarete late afternoon for the beach and night time there. Playa Grande is an awesome beach, further east of Cabarete. You may consider renting a car as all these places are within less than a two hour drive.