For info on Queenstown parking charges go to queenstownairport.com where you'll find a parking fee calculator.
Parking facilities are not fantastic but you'll find ATC helpful. They get lots of itinerants, usually in bizjets.
If you are thinking of flying to Milford Sound have a chat to the instructors at the Wakatipu Aero Club first. It's a spectacular but very challenging environment and Milford is one place where local knowledge is vital.