Santo Domingo is not just safe, but pleasant and a wonderful place to live.
Sure, the power interruptions and the traffic are a neusance, but the reality is that power outages are easily fixed with a "planta" or are taken in stride and the traffic has a sense of gamesmenship!
What's left is a city with strong culture allure, rich historic sites, wonderful tree lined streets, and an urban culture and nightlife to rival any major city in the world.
When it comes to crimes, its very safe. Sure, the newspapers show a couple of crimes that are commited everyday somewhere in town, but these are only a couple of crimes in a city that is home to more than 3 million people and at any given time has a few thousand tourists!
If this is your first time in SDQ, I suggest you stay in one of the large Malecon Hotels (ie. Jaragua, V Centenario, as of Jan 2005 the Hilton Santo Domingo). These hotels are close to the major tourist sites in the Colonial Zone and Gascue neighborhoods and they have everything you could ask for.
For example, you could spend the day exploring the colonial zone. In the evenings you head back to your hotel and freshen up and then go down to the ground floor and pick your entertainment or dining option (many of these hotels have tons of restaurants, shops, casinos, within their premises. The Hilton will be attached to the newest and most luxurious shopping mall in the City, Malecon Center). After having a nice night fun, all you have to do is hop on the elevator and off to your room you go, not worrying of any petty theft, etc.
Overall, the Dominican capital is very safe, varied, and exciting. The only down side is that there is no beach to speak of here, the nearest patch of heavenly white sand is 30 minutes east of the city. Anyhow, the city offers so much (from expansive botanical gardens to unique shops to interesting museums to some of the most expressive people you will ever meet) that the desire for that patch of sand may not be as urgent as initially thought.
Come and enjoy!
To help you plan your stay (and during your stay), refer to this link...
http://www.dominicanrepublic.com/santodomingo/