One more thing. If you want to get around cheap and easy and meet a lot of fun people at the same time: hitchhike!!! It's really easy to get a ride, it's probably the safest country in the world to hitch, and people are generally really nice. Often they do detours just to get you where you want to go. I did a lot of hitching in New Zealand and never had any problems, even though I was a single girl.
I thought you might find the following information useful. I was looking at the following website http://www.theonering.net/index.shtml - under Red Carpet LOTR Locations Day Nine. It lists very detailed locations for LOTR locations that you may not want to miss. I would like to see Martinsbourough and Fernside outside of Wellington just because I am a LOTR fan. Ian Brodie has an exended edition of the LOTR locations and how to get to them if you like to check it out.
I was also reading about the west coast of the South Island south of Christchurch. The Maroaki Boulders and the blue penguins at sunset sound like a sight to see even though I heard it can get jammed with cars. I did a web search on New Zealand vacations and found a family who listed their entire vacation itinerary for the North and South island. I think Flock Hill east Franz Glacier may be worth checking out.
Only one person has mentioned the Coromandel peninsula - I'm shocked. I'm there at the moment and it's stunning please don't miss it. Especially Cathedral Cove and hot water beach - at sunset it's gorgeous.
Also, Raglan (west of Hamilton) little surf town that's really nice (even if you're not a surfer).
And the Catlins (south coast of the south island). If you've got time, head that way but it's easiest to do this by car.
everyone else has covered all the other places so no need to repeat them. Have an excellent time. Wherever you decide to go you wont be disappointed.