Hi there.
You ought to check in on the site from Centers for Disease Control, USA (follow link below). They - and you own doctor, never forget him or her - can give you the best advice.
The few standard rules are: Malaria prophylaxis is not necessary unless you are going to stay overnight in rural areas or very close to the Haitian border.
Don't drink water unless it is boiled or purified. Bottled water is available everywhere and the water at your hotel and restaurants should be safe enough too. The same goes for ice cubes in most places. If you buy from very little local places or street vendors consider buying drinks without ice cubes. Nothing beats a cold Presidente beer anyway!
It is generally a very good idea to get vaccinated against Hepatitis A. The disease is usually not very severe, but unpleasant enough, and it is easily avoided by for instance a quick shot of immune globuline. The reason that you should get vaccinated against Hep. A and not the other sorts of hepatitis is that it spreads very easily through for instance water and food.
And generally you should consider getting vaccinated against diphteria and tetanus, both of which can be fatal.
The Dominican Republic does not have a lot of health problems. So what is mentioned above is more or less the standard "leaving the industrialised world" recommendations.
One more thing that a lot of foreigners forget: Measles are very common in most countries, including the Dominican Republic. If you bring unvaccinated children to the island, be aware of this. Measles are normally not a problem but in a very few cases they can cause diseases which are severe and even the hardiest children tend to get pretty ill from measles also when it isn't serious.
But generally: Enjoy yourself. This is not a country where strange and exotic tropical diseases lurk around every corner.
Regards, Susanne