There are 3 main tourist areas in the Dominican Republic, they are several hours drive apart and all have different international airports.
Do a search on a map of the Dominican Republic so that you can get an idea.
To summarize:
The North Coast is served by the Puerto Plata airport. This area includes Luperon, Sosua, Cofresi, Maimon, Cabarete, and obviously PoP. Ocean World is located in Cofresi between Puerto Plata and Maimon.
The East Coast is Punta Cana/Bavaro and it has its own airport. Manati Park is located there.
The south is Santo Domingo, Bayahibe, La Romana and Juan Dolio. They have Santo Domingo and La Romana airports.