Punta Cana International Airport is the nearest airport to Higuey (aprox. 60 km). As an alternative you can fly into La Romana Airport or Santo Domingo’s Las Americas International Airport.
There are taxi and bus services from Punta Cana International Airport, Santo Domingo and La Romana to Higuey. When visiting Higuey for just a day or two I prefer to rent a car, which gives me the maximum amount of freedom