Do the following:
1. Get a map of Santo Domingo.
2. With a marker, highlight the following avenues:
Start at the Zoologico Nacional in the northern part of the city, highlight Avenida Tiradentes from the Zoologico area down to where it intersects Avenida Kennedy.
Highlight Avenida Kennedy from the intersection with Tiradentes to the right to where it meets with Avenida San Martin.
Highlight Av. San Martin from the intersection with Kennedy and V Centenario all the way to where it meets with Avenida Mexico.
Highlight Av. Mexico from the intersection with San Martin all the way to the Puente Mella over the Ozama River.
Every neighborhood north from the highlighted avenues should be avoided. Every neighborhood there is not particularly dangerous, but the most dangerous of the capital are in that area. Much of the area is rundown, the infrastructure is in need of upgrade. The only difference is when you go from a poor neighborhood to a really poor neighborhood the buildings shift from cement to wood.
Since it would be hard for a tourist to tell apart to relatively "good" areas from the hell holes, its best to avoid them all.
However, everything north of Avenida Mexico up to Calle Paris comprises the San Carlos and Villa Francisca neighborhoods. The Villa Francisca is also known as Peque?o Haiti since its the unofficial center of the Haitian expatriate community in the DR. Those areas, although rundown, can be safe during the day, so if you feel like going there you could with a guide. Don't even think about doing so by yourself or at night.
The rest of SD is much safer than the areas denoted above, but as always, remember you are not just in any city, but in a metropolis of 3 million people. As in any metropolis in the world, be wary of your sorroundings and who is around you. Nothing to panic about, nothing to really worry about, simply keep your common sense on guard as if you were visiting any major city in the U.S. or Europe for that matter.
Another tip would be to never jump into a taxi or into a Carro Publico or even a guagua. Most people are nice, but all you need is one bad apple to ruin your stay. Best avoid those methods of transport than running the risk of being sorry later on. If you need a taxi, call them from a phone and they should pick you up. If you tell your taxi driver to wait for you until you come out of some museum or shopping center, etc. they usually would do such.
Don't rent a car to drive in the city. Driving in Santo Domingo is not for the faint of heart. Plus, parking can be a problem in many places. Only rent a car if you want to rent a car for exploring the rest of the country.
Keep in mind that Autopista Duarte is the most heavily used highway in the country, so perhaps if you have to use such highway it would be best to take a Metro bus rather than rent a car. If, however, you are heading east or west of the capital, renting a car could be a pleasant experience. Those roads tend to be sparsely traveled making a drive in most places in the east or south a pleasurable experience, although be aware that maniacs abound anywhere you go in the country.
Enjoy your trip!
-NALs