The cheapest and fastest way to get to the Balaji Palace is to fly to Puerto Plata Airport (POP) aka Gregorio Luperon International Airport, in Puerto Plata, Dominican Republic. Puerto Plata Airport is actually about 1 hour, 15 minutes from The Palace.
Miami, JFK, Chicago, Newark, San Juan has direct air into Puerto Plata.
From Puerto Plata Airport (POP), a helicopter transport for up to 3 passengers with light or carry on luggage is $1500 USD each way. Check with Balaji Palace on helicopter flight fees from the other airports.