Non-Track Tramps

Also, we are based in Auckland. So a North Island option is best.

Ruapehu/Tongariro has plenty of scope for nice off track travel. Anything further north would most likely involve a lot of bush bashing.
Also have a look at the Umukarikari-Thunderbolt loop in the Kaimanawas as it has 1 day of off-track travel. Not a good option in low visibility.

http://tramper.co.nz/?6073

Description of the Thunderbolt route

Second both of these suggestions.

For Kaimanawas, Waipakihi River is also good.
For Tongarairo a fav trip is Mangetopopo, south crater, traverse anticlockwise around Ngaurahoe to the tarn above Upper Tama, nice camping in a canyon there. Then either drop down to Tama and return via track, or follow the long ridge down to Waihohonu and return via crossing or push a route up the lava flow above Oturere to south crater.

For some other really neat country try the Ruahines. We had a fantastic four days in the southern area in a whiteout using GPS the whole way. Iron Gate, Triangle, ridge to Howletts and back. Bit of river bashing to Triangle!