Be sure to check that there is adequate coverage if you rent from the local operators and that there is a spare tire and jack for repairs. Another alternative is the rental of motorbikes that are available in all sizes in major tourist centres. Available in all major populated areas at fixed rates which are considerable higher than prices for public transportation. Beware because some drivers may attempt to overcharge you thinking you don't know the price, so insist on knowing the price before entering the vehicle, and enquire from your hotel in advance, if possible. There are several competing radio-dispatched taxi companies operating in Santo Domingo and Santiago, and a few in smaller cities and resort areas such as Puerto Plata, which also charge fixed rates.
Prices are a bit higher at night.
The Dominican Republic has a very extensive public transportation system, most of which is provided by buses. Shirt-sleeves or light sweaters recommended, because temperature controls are often set to very cool. There are also several other smaller regional carriers which utilize smaller buses. In the cities, they travel along major arteries or on fixed routes from the outskirts to major points in the centre, such as Plaza Independencia or Parque Enriquillo, for very low prices. They have no fixed stops for picking up passengers, so all you have to do is wave them down.