Castlegar airport (YCG) is only 40 km from Nelson. There are several flights daily from Vancouver, and one flight daily from Calgary, all with Air Canada. Air Canada also fly into Cranbrook (3hrs to Nelson by car) and Kelowna (4.5hrs to Nelson by car).
From Castlegar airport Queen City Shuttles operate a shuttle service that meet every flight and can drop you at The WhiteHouse. Advance bookings can also be arranged. In case of flight cancellations in/out of Castlegar Queen city Shuttle also operate a service to Kelowna Airport (minimum number of passengers required to operate service).
Pacific Coastal Airlines have a regular service from Vancouver to Trail, 69kms from Nelson.
Spokane airport (GEG) is 3.5 hours from Nelson. Queen City Shuttles also picks up from this airport for small groups with prior booking only. Car hire from Spokane Airport may be another option.