The Cap Cana/Punta Cana Airport is known as PUJ - Punta Cana International Airport. It is 15 minutes from Sanctuary!
There are plenty of taxi services from the airport (PUJ) that take you straight to Sanctuary. We also recommend the taxi service called "Amstar" - it is super easy & completely online. You can book prior to your departure to have them ready upon your arrival.
Sanctuary's room block with us is a minimum of 2 nights at a discounted rate. The link to reserve rooms will be available soon.
As an American Citizen, you can easily arrive to the island with a valid passport. If you have a different citizenship, we recommend contacting the Dominican Consulate in NYC for visa requirements. Contact information: https://migrantinfo.iom.int/en/node/3019