Depending on when you get to Santo Domingo, you can either head for Sosua the same day or spend the night and go the next day.
One possibility is a taxi. That will cost you about RD$2000, approx. US$80 at present rate of exchange. Another is to rent a car.
The third option is to take a Caribe Tour bus. These are modern, airconditioned buses. Very comfortable. The price is approx RD$120 to Sosua, about US$5. There are buses leaving for Sosua every hour from 6 am in the morning until the last bus which leaves at 6 pm. The trip to Sosua takes about 4.5 hours, including a 20 minute stop in Santiago where you can get something to eat and drink.
