Queenstown is where bungy jumping was pioneered by AJ Hackett and the first commercial jump started in 1988 at the Kawarau Bridge (on the main road into Queenstown from the east). If a bungy jump is on your 'to do' list them Queenstown is the place and the Kawarau Bridge is a 43 metre jump from an historic bridge with an optional 'dip' in the Kawarau River.
It is important you read and understand the risks associated with this activity. For more information see here.