Yes, there is a quirky little store in Puerto Plata where you can buy guitars and strings. It is somewhere around Bornigal Hospital, on a road on the right heading up the hill. Stop and ask someone when you are in that area.
I was in La Sirena today and they do have a small selection of strings in the electronics counter display. I purchased a Yamaha C70 classical guitar at La Sirena a few years ago and it continues to be a great sounding guitar.