For HOW LONG???
Rough Location/facilities?? Near a barrio or in the RICH part??
Apartments are normaly rented by the 3 month period but some are available for 1 month if you know where to look. If you are looking for a TWO week booking, you might like to try the Puerto Plata Beach Resort Apartments on the Malecon, 1 x bedroom & lounge with "put-you-up" sofa/bed!! US $22 per night (poss US $20 per night for 2 week stay!!) - Grahame.
Why don't you stay at Sofy's B&B or condos dominicano, or that place Jazzy stays at - until his place is built.
That will give you a chance to hunt for a longer term place that you can see, and the area you are looking for.
Sofy's is walking distance to the malecon.