We recommend flying into Nashville International Airport (BNA). Nashville is a large city with many connections to/from other airports.
Nashville Airport is approximately an hour and a half from Burdoc Farms.
An alternative option is to fly into Evansville Regional Airport (EVV). Evansville Regional is a much smaller airport that may not offer connections to/from some airports, but may be cheaper.
Evansville Airport is approximately an hour and a half from Burdoc Farms.
We definitely recommend renting a vehicle if you will be flying in to get to the venue and explore what the Nashville and western Kentucky area has to offer. Both airport options provide several rental companies on site.
Additionally, you can look into third-party sites like Turo.