Where to start!
There are Dominican organisations working in many areas of development, to which you would be able to donate. Ensuring that your money has been spent effectively is another thing though.
I can provide a list of local NGOs working in a range of thematic areas: environment, women, health, elderly people, disabled people, children, community water provision, forestry management, sustainable agriculture, promoting organics, citizen participation and decentralisation, civil rights, and more. I know several of these from direct experience, or have friends who work or have worked there.
On the international side, many large and well-known organisations have programmes in the DR. There is an issue with running costs, I know from first hand that they are by definition large bureaucracies, but they are transparent and accountable, in that they will produce credible annual accounts that tell you exactly where the money has gone, and have a ceiling on what percentage goes on admin.
International organisations with programmes in the country range from large UN agencies like UNICEF and governmental aid bodies like USAID and the British DFID (via the embassy), the Canadian, the German GTZ and the Swiss Helvetas. Other organisations with a presence here include Oxfam International, headed by the Spanish Oxfam Intermon, CIIR/ICD a British organisation I worked for briefly which places volunteers in community projects, and several others like World Vision.
All of these are easily accessible on the web, but let me know if you would like more specific information.
I would urge caution and first-and research with any organisation that you are considering as a beneficiary. Many are excellent and full of commited people who work all hours doing effective work, others are... ya tu sabes...
You would have to meet with them in person if you are considering a serious donor relationship, and would have to make regular visits or nominate someone in situ to do this for you. You would have to ask for annual audited accounts, and progress reports.
The difference with donating through a large organisation is that they would do all this for you - hence the operating costs. For a donation to be effective, all this is essential, otherwise you are running the risk of the money going to the director's jeepeta fund!
The decision is yours: either donate to an organisation that spends, say, 85% of your money on the project and 15% on admin reliably, or gamble 100% of your money with a project that might or might not be putting it to the intended use.
Chiri