Edoras
Where they filmed Edoras is Mt Sunday. About one and a half hour drive south from Christchurch you can find this beautiful location. Only way there is a gravel road, but when you see it you will not regret it.
Anduin River
Near Te Anau you can find a hiking trail called Kepler Track. Around this track you can see a few different filming locations for the river Anduin. Some of them visible from the beginning of the track and others half a day's hike into the Kepler Track.
Ithilien
A short drive from Queenstown on the way towards Glenorchy you can find a small camp ground where Frodo and Sam got a look at the oliphaunt. 12 Mile Delta is the name of the camp ground for an easy reference point.
Warg Riders
Overlooking Queenstown, almost visible from all around town is Kelvin Heights Park. This is where they shot the warg rider attack movie scene and a few other scenes of Rohan.
"The beacons are lit"
Driving along the eastern coast of the south island you come across Franz Josef Glacier. The surrounding peaks of this glacier were used in the beacons section of the movie when “hope has been kindled” as Gandalf proclaims. There are beautiful hiking trails here as many other locations.
Isengard
Hiking the Earnslaw Burn Track located just outside of Glenorchy you get to see beautiful nature that was used for scenes of both Isengard and Ithilien. If you don’t like hiking they have helicopter tours originating from Queenstown that can also take you there.