Flying into Cherry Capitol Airport (TVC) in Traverse City is your best bet. A few locations offer direct flights to TVC (BOS, EWR, DCA), but many options will have a layover in Chicago or Detroit. It's a half-hour drive to White Birch Lodge from there, and there are taxi services available. We don't recommend relying on Uber/Lyft.
Flying into Gerald R. Ford International Airport (GRR) in Grand Rapids is another option, although it would require renting a car. Grand Rapids is 2.5 hours south of Elk Rapids.
For the road warriors among you, there will be plenty of parking at White Birch Lodge. Elk Rapids is a cool 13 hours from Northampton via Canada if you're coming from the East Coast and feel like going that route.