Is it "board" surfing that you are asking about? Yes, there are great waves in the Dominican Republic.
The north coast has large winter swells west of Cabarete, in Puerto Plata, and west of Las Terrenas.
In the summer the south coast, near Boca Chica or Barahona, are the places to be.
There is even consistent surf in downtown Santo Domingo with a dozen people out on a good six foot day, but the water is polluted. This time of the year check out the Boca Chica area for a Rincon-type long right over shallow reef, or Barruco near Barahona for a crashing rivermouth. Other spots include Embassy Beach, a pounding beachbreak in small cove--an hour from the capital and best for boogieboards; the beachfront in San Pedro de Marcoris; or reef breaks in the western part of Juan Dolio.
There are dozens of other breaks that take a four-wheel drive vehicle or boat to find. Some Dominicans are world-class surfers. You won't find crowds except near the capital (Santo Domingo population: 3,000,000) or on holidays.
