Well, I live in the Dominican Republic! I hope I can be of help.
Unfortunatley, I live in Santo Domingo (the capital) and it is quite a few hours away from Puerto Plata.
Don’t worry about the beaches or the people, both are very nice. I’ve been to beaches in Mexico, Puerto Rico and various of the other, smaller carribean Islands, and I find that the Dominican Beaches are better.
Our most famous Rum here is Brugal. It is very good, but I don’t like Rum so I really can’t tell you much more about it. What I can recommend is our national beer, Presidente. I know of few people (if any), that once having tried a beer say that any other beer is better. Do try this beer, it might change your life 
I will get back at you with the Cigar info. I am not a Cigar smoker, but I do have a friend that is quite passionate about them.
In terms of food, give Mangu a tried (smashed plantains), you might like it. Our national plate, however, is “La Badera” which is Rice with beans and meat. It’s hard to go wrong when ordering this plate…
However, are you only going to stay in Puerto Plata, or are you going to visit other areas in the island?
Of the top of my head, near Puerto Plata there is this nice animal/cultural park called “Manati Park”, defintley go visit that, your kids will like it.
Very close from Puerto Plata is Cap Cana, the next great luxury beach resort in the carribean. It has various golf courses designed Jack Niclaus and has awsome vilas and beaches. It is still a working project, but visitors can come and take a look. It would be interesting, and it you can afford to go visit for a day, do that.