The weather has been discussed in some detail previously, so if you want a more elaborate answer you could try the archives.
For a short answer: The Punta Cana/Bavaro area is generally fairly dry and sunny in December whereas Puerto Plata and surroundings tend to be wetter in November, December and January. Even in Punta Cana you are likely to get a heavy shower now and again but they are usually short lived.
Enjoy your holiday.
Regards,
Susanne
