I was able to go down to NZ for a couple of weeks last year, and it was amazing. A friend and I rented a campervan in Auckland and drove our way down the North and South islands, ending in Christchurch. Depending on what you want to do, I would allow as much time as you can afford - 2 weeks wasn't nearly long enough to see everything!
Sorry if someone else mentioned this, but if you want to focus on Lord of the Rings stuff, you should pick up The Lord of the Rings Location Guidebook by Ian Brodie - it's got quite a lot of good stuff in it. There are also lots of tours you can take (and with some of the filming locations, that's the only way you can see them) - Red Carpet Tours is the most highly recommended. If you go during NZ's 'winter' (which would be our summer) you can probably find cheaper airfare, but the weather might not be that great.
The one big thing I can tell you if you plan to drive from place to place - even though New Zealand is fairly small, and the distances look pretty close together, it will take you longer than you think to drive, due to lots of windey roads and mountains, so plan accordingly!
I was hoping to go back this year, but alas, it doesn't look like I can, so hopefully next year. Good luck with your planning, and if there is anything specific you'd like to know about my trip, please feel free to send me a private message.