NZ Treks

You probably know that there are the great walks. You can compare them to start with here. You could do the combined Greenstone/Routeburn walk which takes about 6 days and takes you thru some beautiful alpine scenery and then maybe do the Queen Charlotte Track or another coastal one for variety?
At that time of year I imagine most of the tracks would be pretty crowded so, on the other hand, it may be best to go for a less popular track.

If you want a track around the ocean then go to Stewart island . You could try the Northwest Circuit.

You could try to get a copy of Moirs Guide (2 vols - N and S) - the best guide book to all the mountain areas of the southern half of the SI.

I gather you are looking for something a little more challenging than a Great Walk. In the North Island I have two suggestions. Firstly, the loop track in the Whirinaki Forest is very nice and a touch remote. Takes 4 to 5 days, with transport available nearby. Its handy to Rotorua and Taupo. Another more strenuous North Island suggestion is to walk from near Napier to Turangi, or vice versa. This takes 6 to 7 days, and includes some tops and rivers. Plenty on offer down south. Check out Wilkins Young area ( north of Wanaka), Nelson Lakes or Kahurangi ( near Nelson) for some challenging options. Good luck.

Sounds as if you're looking for something long, hard and remote. If that's the case, you can't beat the Northwest Circuit on Stewart Island. Very remote, hard going, muddy, very few people, fantastic forests, beaches and even some awesome mountain views as well. If you're lucky you will see kiwis in the wild. This is as close as you can get to a true wilderness experience whilst still being on a marked track. About 10 days is a reasonable time frame, or add an extra one to climb Mount Anglem, the highest point on the island.

Other suggestions:

Dusky Track
Wangapeka/Leslie-Karamea/Mount Arthur Tablelands in Kahurangi NP
North-South traverse of the Kaimanawas, Kawekas and Ruahines on the North Island.

I think Moirs Guides are more for off-track route planning, but if you're confident enough to just head out into the wilderness with no tracks, then go for it!

If you are in the north island, you could combine the Tongariro northern circuit and the Round the mountain track for a walk of about 7 days, moving for between 4 and 6 hours per day.

Murray