There are many ways to get around Puerto Plata, all which are perfectly safe.

Taxis are always readily available either outside the main entrance of your hotel or a short walk away in front of the plaza in Playa Dorada.  They are usually pretty cheap, although the ones at your hotel usually charge a bit more.  It is a good idea to negotiate a price before you get in so there isn't any confusion.  As with all things in Puerto Plata, it is advisable to bargain with them.  A ride that would cost around $7-10 in Canada would probably be only $3-5 there.

Another even cheaper way to get around is the moto-taxi. This is a motorbike which usually fits a driver and two passengers. They are always waiting outside the Playa Dorada complex gates. Also a good idea to negoitate price before going anywhere. Usually it is a bit more for 2 people than one, but it is cheaper than taking a taxi and sometimes quicker.

There are also the public cars, which are great if you want to go more of a distance for cheaper. This is a car filled with as many people as it can fit and they leave from designated places every so often.  You can probably ask around to find out where to catch one. They usually cost about 40 pesos per person for each car you take.  For example, it may take you 2 cars to get from Puerto Plata to Sousa as each car only goes a portion of the way to meet another car to get you to your final destination.