I'll try and help...
Northern Brown Kiwi - Guided tours in Trounson park, Northland. Best way is to go back out again on your own after the tour is over. Weather can be important - chucking it down when I was there and dipped (good views of Morepork though)
Little Spotted Kiwi - on Kapiti - didn't go there so can't help. Apparently the boat trip to Kapiti is very weather dependant and it's quite possible to fail to get over (or be late getting back)
New Zealand Little Grebe - saw in various locations, e.g. Waiwera sewage ponds, Rotorua area.
Black Petrel - Hauraki Gulf pelagic, I think reasonably reliable but our trip was cancelled so I can't be certain. Wrybill tours and Pterodroma pelagics run trips.
Pyrcofts Petrel - There is a specialist pelagic for this on the Wrybill tours website, can't remember any specific details at the moment. Otherwise I think pretty unlikely.
NZ Storm Petrel - Same as for Black Petrel. I think this species is pretty reliable these days!
Blue Duck - well known site near Ruatiti. We wasted a lot of time looking around Turangi seeing bugger all, so I wouldn't recommend that. Go to the place that everyone goes to.
Brown Teal - non re-intro populations - only saw one, on Tiri Tiri Matangi (presumably introduced). Helena Bay is the well known mainland site but it's quite a long way north, we didn't get that far.
Takahe - longest established - is this Kapiti or Maud? - no idea, only saw it on Tiri Tiri.
NZ Dotterel - easy on the beaches at Waiwera and Wenderholm. Also saw a couple at Waipu and one at Miranda.
Whitehead - quite a lot on Tiri Tiri, otherwise the only one we saw was at the campsite at Pureora forest park (can't remember the name, but it was not far from the Totara walk, you pass it when approaching the forest park HQ.
Kokako - non re-intro populations - no idea, dipped it. Pureora is supposed to have some but very difficult I think.
North Island Saddleback - longest established population? Is the native popualtion on Hen and Chickens viewable from a zodiac? - can't help, only saw it on Tiri Tiri.
Stichbird - access to Little Barrier for native population - ditto
We bought a customised itinerary from the Wrybill tour guys. Probably not essential if you know NZ at all, but it was very useful for New Zealand first-timers like me.