There are, to my knowledge, 2 really great men working in caoba here in Puerto Plata. Of course there are more, I just happen to know of these. Handmade is expensive, good quality and unique.
In Puerto Plata, you can also find some good items at Hidelisa Muebles and Gonzalez if you´re looking for that kind of furniture.
If you want lighter there is a new shop with classy Italian style that has opened behind the police station.
There is a good rattan craftworker here in Puerto Plata as well, on Calle Sanchez, close to the firestation.
In general on the island, my opinion is that there is no place that is best on all items. Your best bet would be to look around, see what you find for the day ( as it always depends - here today, tomorrow not )...
Good luck!!