Hello - I spent almost a year in NZ in 2000, primarily on the South Island. Some of the things that I really enjoyed and that I would highly recommend:
3 day kayak trip in Doubtful Sound - I went with Fiordland Wilderness Adventures, and it was incredible. Absolutely stunning scenery, tonnes of wildlife including penguins and seals, camping in beautiful temperate rainforest, and fantastic, friendly guides. All the necessary equipment is provided, and by all standards it has to be considered great value for your $$. Definitely top of my list of things to experience while in NZ. Just watch out for those sandflies.
Dolphin swimming in Kaikoura - my group got lucky, the boat operators managed to find a huge pod of dusky dolphins the day I went out and we were able to get in front of their path multiple times; snorkelling in the ocean with those hundreds of silver flashes going by beneath and beside you, seeing them jump and flip, words can't describe the experience.
Hopefully you can avoid getting seasick as I did.
Picton, Marlborough Sounds - a beautiful, quaint town in which to spend a day or two. Great scenery, a necessary stop if you are taking the ferry to the North Island.
Skydiving - if you are going to do it, do it in NZ. It has got to be the cheapest in the world. I went in Taupo for around $140 NZ for a jump from 12,000 feet. Ditto bungi jumping, which I never did and have lived to regret. If you are in Queenstown and are into that sort of thing, do the jump.
Some of the areas of New Zealand the I most enjoyed were the least commercial - tourist oriented. A slow drive down the west coast from Nelson to the glaciers and farther south reveals lots of interesting and unique stops, ie. the hippie communes, forgotten outposts, etc.
Go walking anywhere - there are paths/tracks everywhere, by every town, often leading to hidden and majestic vistas. Just be careful and prepared, use a map. The Canterbury highlands, the southern lakes region, also both magnificent.
I could go on for pages. If you enjoy the great outdoors, even if you are not experienced in it, the country offers something that will make your visit enjoyable and memorable. I thoroughly enjoyed my time there.