Not a kiwi myself, but i had a great trip in January/february last year with majority of endemics photographed (including three kiwis (the bird)). Reservations for migratory patterns i've forgotten. I'm sure i will be corrected.
Ulva Is. off Stewart Island is great for SI Saddleback, Yellowhead, Red & Yellow-crowned Parakeet and Weka.The football field behind Oban town is great for South Island Brown Kiwi
I had Yellow-eyed Penguin, Stewart Island Shag, and Spotted Shag (punctatus) at Bushy Beach.
Orokonui near Dunedin: South Island Takahe, Fernbird (punctatus), New Zealand Kaka (South), New Zealand Robin (australis), Rifleman (chloris), Tomtit (macrocephala)
A boat tour in Marlborough Sounds should give you NZ King Shag.
East Homer Tunnel will give you Kea and South Island Wren.
Tiritiri is a must! Little Spotted Kiwi North Island Kokako, Brown teal (pāteke), Stitchbird (cincta), North Island saddleback, Whitehead (popokatea)
North Island Brown Kiwi is found at Tawharanui Regional Park
Shore Plover is at Motutapu Is. off Auckland.
NZ Grebe, Wrybill, and Red-breasted Dotterel (as well as a lot of the more common waders such as oystercatchers is at Ambury Regional park and Mangere WTP
Here are the birds that i missed: Pycroft's petrel, New Zealand Storm Petrel, Parkinson's Petrel (these birds will require a North Island Pelagic, didn't go). Black stilt ([kaki], at Tasman Delta, didn't go). Malherbe's parakeet and Great spotted kiwi (at Arthurs Pass, didn't go). Blue duck (Fiordlands NP, missed, hurts). Fiordland penguin ([tawaki], I went on a two day one night cruise in Doubtful Sound and still missed. Apparently this is a very seasonal bird.), Okarito brown kiwi (Heard only, near Okarito). New Zealand Falcon found all over, and definitely hurts the most.
Do not cheat yourself for a trip with Gary for pelagics out of Kaikoura! Albatrosses, Shearwaters and Petrels en masse.