I live in Zona Colonial and I feel very safe and I think that most of Gazcue is safe also and around the US embassy and Bella Vista .Piantini and Naco are probably safe but the traffic there is horrific.
The safest place IMO in the entire city is Zona Universitaria, mass security 24/7 everywhere, very little crime at all.
Everywhwere has safe and unsafe parts to it so you can't really call and entire Zona or Area overall safe. You need to drive around for 5 or 6 hours one sunday then again on a weekday and see where you feel comfortable. The city is very easy to get the feel of within minutes of entering different parts/streets/zones.
I wouldn't automatically go with price being safer, not always the case.
Thank you for the responses. In searching the forums I have read about power outages and need for generator backups. Is this a regular occurrence in these areas mentioned above, how often and for how long do they occur? I guess I'm really wondering is it long enough that food in the freezer or refrigerator spoils?
Also what is a better/safer choice for a mother staying home with a child during the day, a house in a neighborhood or a condo/apartment?
What should we expect to pay in rent for a 2-3 bedroom home in these areas?
On the question of power - practically everywhere you live you will need an inverter or a generator. Power rarely goes out long enough to exhaust the inverter batteries except for in exceptional circumstances such as hurricanes and tropical storms.
See if you can find anything in the Anacaona apartment complexes in Mirador Sur, set in gardens with pools and kids' play areas. Rentals are in the US$1000+ range, depending on whether it is furnished/unfurnished, location and condition of apartment.
Some are in better nick than others - the complexes were built in the late 1970s. The ones closest to the Anacaona Avenue are the least desirable due to traffic noise.
The location of the complexes is close to the city's main park, good shops, supermarkets, restaurants, mall/cinema, pre-schools and schools. 10-15 minute drive from the main city centre.
I can put you in touch with someone who would know of anything that's available for rent, so if you're interested send me a private message.
If you take a note of where most of the embassy residences are that gives you a good gauge, and most are in Cerros de Arroyo Hondo. An absolute traffic nightmare morning and night, which puts a lot of people off, but open spaces, greenery, closed communities, guaranteed that you don't have 56 apartments which look down on your garden etc.... and priced in the same range for a 400m house with gardens, as a 250m new apartment in Naco/Piantini etc...(RD$8-RD12m)
I feel very safe with my family, including young children, in the neighborhoods along the Mirador Sur park, such as Bella Vista. I would recommend a condo, as it will have both a doorman and often a large generator for power outages. But as others have written - this has a lot to do with preferences...