The NH is the name of the hotel, but I don't think it has a pool. I agree with Cap N Glen. Loads of condos available right now as the high season is ending. You can probably get a one bedroom for around 500 a month or a two for 800 right now. Prices subject to change from one building to the next. PM me if you want an opinion on any of the complexes around here. I know most of them. Some are nice, others seem to have a lot of pool problems. All are within a walk to the beach, restaurants ect.
Renting in true punta cana, much more expensive, but thats a personal choice.