Anita: You are obviously a NEWBIE to driving in the DR. We have posted some very funny and some very tragic stories of driving here.
I would suggest you first do as we suggest: Take a taxi to the Metro or Caribe Tour bus station and then, when you are in Puerto Plata (where, exactly are you going?**) you can decide if you want to rent a vehicle.
** I ask this because while the province of Puerto Plata is quite large the city is rather small and unique in its history. However, many hotels advertize themselves as being in Puerto Plata, but are really in Maimon, Sosúa or Cabarete, or even somewhere in between...
THEREFORE, if you are going to Playa Dorada, no problem, take the Metro to Puerto Plata and then a taxi to your hotel.
However, if you are going further east, like Sosúa or Cabarete, you are best advised to take the Caribe Tour bus to Sosúa and then taxi to your hotel.
Remember, always ask and agree upon the price before any taxi ride. At the airport the going rates are posted, and I do believe that at the taxi stands in Puerto Plata and Sosúa they are posted as well.....
Good luck and let us know how it goes...
HB