Rhinelander–Oneida County Airport: The closest practical airport, about 30–35 minutes by rental car to downtown Minocqua. There is no dependable scheduled airport-to-Minocqua public transport to plan around; reserve a car or arrange a taxi/private pickup before you land. A rental is usually the sensible choice for a stay here.
Central Wisconsin Airport, Mosinee: A workable alternative with more flight options, but it is a roughly 1 hour 20 minute drive to Minocqua. Rent at the airport; the evidence does not support a useful direct bus or shuttle. Expect rental-car pricing to vary sharply in summer and on holiday weekends.