By "Santo Domingo" do you mean the city? There are not very many beaches there.
For an off-resort civil wedding on any beach in the country you have the option of getting the judge (for an extra payment) to go there to perform the ceremony. For example, I got married on the beach at Las Galeras, a few months later my husband's cousin got married on Playa Rinc?n, in both cases the ceremony was performed by the judge from Saman?.
Closest to Santo Domingo would be Boca Chica and Juan Dolio to the east or Palenque and Najayo to the south west, combined with a meal for your guests at one of the seafood restaurants after the ceremony.