Mordor was filmed in two locations: Tongariro National Park (which I visited) and the Whakapapa Ski Field (which I visited too). To be honest they’re pretty much the same place.
The book talks about the Grand Chateau, which the crew stayed in during filming, but you pass it on the way to the Whakapapa Ski Field, which is the most identifiable area of Mordor.
After the long drive up to the ski field (on a tarmac-covered road no less), you can park up and go exploring the area on foot. The whole area is reminiscent of Mordor and was used for both the opening battle in FOTR and the climactic battle in ROTK.
GPS would be useful to identify locations precisely and some sturdy boots to cope with the volcanic rocks. Also, this is best seen in the spring/summer months as it’s covered in snow otherwise – as you’d expect with a ski field.