Ithilien Camp was filmed at two locations: Ohakune (which I visited, the point where they filmed is accessible), and Twelve Mile Delta (which I also visited, and is accessible).
Twelve Mile Delta:
Another location a stone’s throw from Queenstown, and on the way to Glenorchy. Twelve Mile Delta is a river delta of stone and pebbles that is mainly used as a camping/fishing area. It’s a Department of Conservation (DOC) camping area and so is open all the time and free to enter. The roads/paths leave something to be desired though.
The area is easy to tie up with a relevant film scene, though difficult to allow you to pinpoint a location precisely.