Personally, I don't believe adventure comes from controlled man made rides providing cheap thrills so I'll let other people talk about things like jetboating or zorbing..
New Zealand is famous for its hiking and climbing so I would suggest one of the many outstanding trails it has to offer. Kepler, Routeburn, Abel Tasman, the Mt Cook area, Mount Taranaki, Tongariro... Climb at least one peak while you are there. Plenty of them are accessible to hikers...
Considering the amount of water, you'd be missing out if you don't go sea kayaking(Marlborough Sound would be good), sailing and maybe even a little surfing or fishing...Whitewater rafting if you're a tourist, if not then go do the real think in a whitewater kayak.
Doing some work on a farm can be interesting if you've never milked a cow or sheared a sheep.