Two routes from bikepacking.com if it helps.
https://bikepacking.com/routes/no-8-wired/
https://bikepacking.com/routes/old-ghost-road/
My daughter did study abroad at Wellington for six months and toured toured the south island by van for two weeks - Christchurch, Queensland, the mountains and fiords, etc. "Daddy, you need to ride your bike there." is what she said.
I'll ask her if she knows anything specific.
-Tim-