In Puerto Plata there is an appart-hotel in front of Jose Luis supermercado that is called Sunny Island Appartments. They have studios for rent on long-term. The owner is Canadian so it's saver in a way for your money... lol.
It's on the main street, busy with taxis, motoconchos and many stores to walk around without paying for transportation. With the mercado just in front, it's a blessing in disguise, since because of that it's somehow noisy during the day but I can live with that. Rent is not expensive and security is good.
Woman in charge is Norma ; 809-586-8376. Give her a call.