When traveling off the major tourism destinations or urban areas you will need cash/pesos for many purchases, including buying arts and crafts from small vendors or fruit from fruit stalls. Go for a fresh coconut water out of the coconut on the road!. For all else... credit cards are best so you travel with less cash. If you need an ATM, use one of these at major shopping malls or stores or the banks themselves.
Better to fill up in a major tourism destination or city and not in a rural area gas station.
As advice has been given... take the local car insurance coverage, despite having coverage on your credit card.
Use Waze for driving here. Google Maps as a back up. Dominicans use Waze domestically a lot and it works well with few exceptions.
Leave very early for all your travels to take advantage of the full day.
If you will be on the road, suggest you buy a pre-paid Internet plan available from Claro or Altice. You want to be connected when on the road.
Why do you like Waze better than Google maps Dolores?