This mountain can be seen in the background of the scene where Legolas shoots down an oliphaunt. The photo is taken from the Tasman Glacier viewpoint, roughly 80 m above ground level.
Click the image to toggle between the original and a colour-graded version that matches the actual film scene.
GPS coordinates: -43.6960, 170.1681
The link opens in Google Maps (desktop) or in the Google Maps App (Android).