La Isabella is a nice place nearby that has some historical significance to one of the "settlements" established by Columbus. We met some artisans who seem to live on site. They make wood carvings - we got several small polished wood carvings of primitive faces (kind of like tiki gods) and a very nice turtle carving. The price was pretty reasonable. I think they threw in the turtle.
The Brugal rum factory has tours.
The Waterfront in Sosua - has a tremendous view!
The road to the beach is lined with street vendors who sell everything, including some very vibrant artwork.
(A word of caution - at most of these places, you will be approached by people selling many different things. They will be persistent. There will also be shoe shine boys. It's best if you have shoes for them to polish, otherwise if you just give them money, they are more likely to realize that begging is another way to get money.)
Take a ride on a guagua. It's a cheap way to get to Sosua - jam packed along with 30 other passengers. Plan to sit on your boyfriend's lap at some point. There's usually a guy hanging out the front passenger side who will stop the driver, collect money, and keep it moving. You tell him where you are going, and he'll tell you how much to pay (check with others to determine ahead of time what is a fair price to pay.)
Cabs in general: get the cost up-front. Everywhere.
There are 2 amber exhibits in Puerto Plata - both worth looking at. One is a museum near the plaza, and they sell amber. The other is on a side street; there is a dinosaur, and at the end of the tour, there was a guy rolling cigars.
There is an awesome fort, and a cable car too. I think they call it the teleferico.
Check out the "malecon": it's the oceanside street.
And plan to sit at a road-side cafe to have a Presidente beer. They might even serve it to you in a bamboo drink cozy. The colder the better.
There's a pretty nice pizza place just up from the ayuntamiento (big white building).
Have fun.
mkohn