wander? would you be walking or driving? There are several areas that should be avoided, but to be more precise you should provide what places you're planning to visit.
as far as wandering on foot goes, get yourself a local phone and program in the number of Apolo taxi 533 0000. Then you can walk around and wander until you are tired, and if you feel too tired or are getting to a place that you do not feel safe, you can call and ask the next safe looking person .. to tell them where you are.. "Digale donde estas, por favor".. or something like that. (My Spanish is more to just get by with.. Dominicans are very polite and do not correct me which is both a good thing and a bad thing) Apolo and most of the cab companies are the best run operations in the city and will be there to meet you inside of three minutes. You can also go inside any colmado and ask them to do this for you.
The taxis can also be hired at 400 pesos an hour which is a great way to sight see.
Alternately, you can get on one of the big buses and just ride it. The passengers will adopt you. There are very few gringos who ride the buses. They will tell you where you are and when you should get off and how to get back to where you were. I did this on a bus going down Av. George Washington and all the folks around me wanted to know where I was going and finally said, No. You have to get out here and take such and such a bus. I had two people who were ready to get out with me and show me the way.
The carros publicos are a lot more tricky since their routes are more complicated and I have never tried to just ride around in them. But if you find one with an empty front seat, you can pay double the fare for two seats and no one will sit next to you. I suppose that you could also follow them to the end of their line. But I like the view from the buses better. Fplks have often have trouble with robberies in them and they stop often and are never air conditioned so not my favorite form of transport.
Cabs from one place to another are never more than 200 pesos. They should be around 170 but cab drivers often do not have change, or so they say.
Nevertheless, you need to see both the Zona and Gazcue and the business district and Parque Mirador Sur and some of the higher end residential areas, the Botanical Gardens, the Zoo, the Museo del Casas Reales, the Modern Art Museum.. a show at the Teatro Nacional... lots of stuff to see.
SD is a very beautiful city but I think that lots of folks get tired out walking or frustrated with the driving. It is hot. And lots of the areas are not set up for walking.
Some of the architecture is stunning and seeing it lit up at night is gorgeous.
enjoy