There is a wide variety of landsapes down in the South Island, from near desert to rain forest. If your daughter is looking for LOTR scenery, then try Glenorchy, near Queenstown. Some was shot there, a lot was shot around Wellington at the bottom of the North Island (where I am, love to meet if you are in this part of the country). How flexabile is your schedue? Are you renting a car/van and driving?