To keep it short, tradition is that on New Years Eve everybody stays with the family till midnight, then the trabucazo blows off, everybody congratulates each other and at 1:00 AM everybody take off to a Disco like Jet Set or Maunaloa (be ready to spend big bucks if that is the case) normally there will be merengueros playing till 4:30 and then at 5:00 AM people go to the Malecon (la lata) to watch the first sunrise of the new year.
Later those who wants to keep the party going go to their house pack their swiming suit, fill their portable refrigerators (neveritas) full of ice and beers or whisky and head to the beach, be it Boca Chica or Playa Caribe or Palenque. Cabanas are usually 110% full in that date (people wait in their cars haciendo turno, and paying money to the staff in the cabana so they could get one before the others) so if you plan to have a private time with a significant other you better go early in the night.
That's a typical end of the year in Santo Domingo.