Map from Google - Dominican_Republic

The Dominican Republic, the eastern part of the island of Hispaniola, has a tropical climate, hot all year round, with a dry season in winter, and a rainy season which goes from late April to October along the eastern and southern coasts, while the northern coast, exposed to the trade winds, is rainy throughout the year, although it experiences a decrease in rainfall from June to September.
Because of the north-east trade winds, which blow from November to March, the north facing slopes are usually wetter than those exposed to the south. The presence of mountain ranges add to the effects of the trade winds, so that some areas have a very humid climate and a lush vegetation, while others are nearly barren.
For example in Azua, on the coast of the Ocoa Bay, only 640 millimetres (25 inches) of rain per year fall, and even less at Lake Enriquillo, closed between the two Sierras; the south-west coast of the province of Pedernales is quite arid as well. On the contrary, in the capital, Santo Domingo, which lies on the southern coast but it's not protected by mountains, rainfall amounts to about 1,450 millimetres (57 inches) per year.
Here is the average precipitation in Santo Domingo.
Average precipitation - Santo Domingo
Santo DomingoJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)65555570190140145175180185100851445

Here is the distribution of the rainfall in Puerto Plata, on the north coast, where the wettest months are even November and December, ie the first months in which the trade winds blow.
Average precipitation - Puerto Plata
Puerto PlataJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)175140130115130507070651102302301515

In the Dominican Republic, as generally in the Caribbean, the rains occur mainly as brief showers and thunderstorms, sometimes intense, moreover they are often concentrated in certain periods, so it may not rain for an entire week even in the rainy season.
In fact, the amount of sunshine is good all year round, especially on the south coast, as can be seen in the following table.
Sunshine - Santo Domingo
Santo DomingoJanFebMarAprMayJunJulAugSepOctNovDec
Sun (hours)788888787777

In Puerto Plata, on the north coast, the sunshine amount is slightly lower, especially in the months when the trade winds blow.
Sunshine - Puerto Plata
Puerto PlataJanFebMarAprMayJunJulAugSepOctNovDec
Sun (hours)677778887766

The temperatures in the Dominican Republic are high throughout the year, at least in the plains. During the summer season, from May to October, the heat is sweltering, while it is more pleasant, but still a little humid, in winter.
Here are the average temperatures of Santo Domingo.
Average temperatures - Santo Domingo
Santo DomingoJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)202020212223232323222120
Max (°C)292930303031313231313130
Min (°F)686868707273737373727068
Max (°F)848486868688889088888886

In the mountainous areas, of course the temperature decreases with altitude. In Constanza, at 1,200 metres (4,000 feet) above sea level, winter nights are cool, in fact average low temperatures are around 9 °C (48 °F), and sometimes can get cold and approach freezing (0 °C or 32 °F), but the days are pleasantly warm, around 23 °C (73 °F), while in summer the temperature ranges from 13 °C (55.5 °F) at night to 26 °C (79 °F) during the day.
If you want to climb the Cordillera Central, maybe up to Pico Duarte, which exceeds 3,000 metres (10,000 ft), it's useful to remember that the temperature decreases by an average of about 6 degrees Celsius for every 1,000 metres (3.3 °F for every 1,000 feet).

Santo Domingo

For swimming, the sea is warm throughout the year: the temperature goes from 26 °C (79 °F) in February and March, to 29 °C (84 °F) between August and October, as we can see from the following table.
Sea temperature - Santo Domingo
Santo DomingoJanFebMarAprMayJunJulAugSepOctNovDec
Sea (°C)272626272728282929292827
Sea (°F)817979818182828484848281

From June to November, the Dominican Republic can be affected by hurricanes, which, however, are most likely between August and October. The destructive hurricanes of category 4 or 5 are very rare, but when they directly hit a particular area, they can cause considerable damage. Tropical storms, less intense than cyclones, are more frequent and hit the country on average once every two years.
The country was hit hard by the "Dominican Republic hurricane" of September 1930, by hurricane David on August 31, 1979, and by hurricane Georges on September 1998.
However, not very intense tropical storms can produce heavy rains in inland mountainous areas as well, which can cause landslides and floods.

When to go

In the inland valleys and along the south coast (see Santo Domingo), the best period goes from December to mid-April.
On the northern coast there is no real dry season, in fact the least rainy season is the period from June to September, which as in the rest of the country is sultry and has the danger of hurricanes; here you can choose the period from February to mid-April. If you want to go in summer, however, you can choose the north coast.

What to pack

From November to April: light clothes, sun hat, sunscreen, a sweatshirt for the evening; for the mountains, jacket, sweater and hiking boots.
From May to October, lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms; jacket, sweatshirt and hiking boots for the mountains.