In my opinion, a mixture of pre-planned adventures interposed with surprise-me days works out well.
On the South Island, Milford and Routeburn are superb. You can go as a backpacker and use their backpacker "huts" ,bring your own everything.
or, you can do the Grand Style, staying in their all-everything "huts". These have meals ,even hot-air drying rooms for your boots and wet clothes. It does rain a lot on the West Coast. There are even private rooms with ensuite available. Yes, you better check out the permit status as these routes are highly regulated. Milford for example, can only be done one-way direction.
There are other treks with varying facilities, but the two above are the most famous.
If you fancy a short 2-3 day crampon adventure, do the Ball Pass hike (and hut) on the side of Mt Cook.
On the North Island, The Tongariro Crossing is perhaps most famous. Day hiking it, or hut overnights in the area are available.
