Getting around Santo Domingo may be difficult if you choose to drive.  Although there are traffic lights and signals, not all locals obey them.  it seems like few traffic laws are obeyed.  Instead, try taking a taxi.  There are taxis everywhere.  Your best bet is to find a taxi, and negotiate the rate with the driver.  Don't just accept the price they give you because most likely, when you start walking away, they will start negotiating with you.  If you are up for an adventure, you can take public transportation. The buses are not labeled and the ride may be rocky, but you will get to where you are going nonetheless.

It may be difficult to tell which cars are, in fact, taxis.  There is supposed to be a placard on the passenger side door.  If there is not, the taxi is probably just a citizen trying to make some extra money.  If you don't want to take chances, have your hotel's phone number handy and they will send one for you.