From a medical standpoint, the DR is generally safe as long as you’re reasonably careful about what you eat and drink. The most common travel-related diseases, such as dysentery and hepatitis, are acquired by consumption of contaminated food and water (typhoid and hepatitis A and B vaccinations should be considered). Only purified water should be used for drinking, brushing your teeth as well as hand washing.
It's worth noting there's a small risk of malaria (in the western provinces and in La Altagracia, including Punta Cana) and dengue fever (in Santiago, inland and north coast). In these areas, long pants and long sleeves, mosquito repellant and bed nets are recommended (dengue bites are during the daytime). It's worth considering a prescription for a malaria prophylaxis like Atovaquone-proguanil, chloroquine, doxycycline, or mefloquine.
Medical care is variable in Santo Domingo and limited elsewhere, although good privately-run clinics and hospitals can be found in and around the more heavily touristy areas. Many doctors and hospitals expect payment in cash, regardless of whether you have travel-health insurance. Modern pharmacies are easy to find in cities and mid-sized towns.
Some internet resources:
Centers for Disease Control (www.cdc.gov/travel) Detailed health overview curated with tips and updated notices.
MD Travel Health (www.mdtravelhealth.com) Complete travel health recommendations for every country, updated daily, at no cost.
Sitata (www.sitata.com) Customized medical reports, pre-trip vaccination recommendations, alerts on disease outbreaks and other breaking health news.
World Health Organization (www.who.int/ith) Available online at no cost as well as in book form – International Travel and Health – which is revised annually.