Not much travelers choose Danang Airport to Phong Nha private transfer. But some cases there are fully booked flight to Dong Hoi Airport and Phu Bai Airport (more closed than Danang Airport) so you have to book flight to Danang city then looking for the best transfer from http://dananglocals.com/package/danang-to-phong-nha-by-private-car. (Best price and best way).
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The distance from Danang to Phong Nha is 342km – 6hours driving by Danang Locals. Some lucky ways, you can catch Vietnam Express Reunification Train from Danang to Dong Hoi for 4,5hours.

Taxi Drivers at Danang Airport they don’t speak English. They will charge your money bases on the distance by metered taxi. While Danang Locals is could be higher cost for your budget so let Danang Locals be your best transportation option for your trip from Danang to Phong Nha.