If your set on the mount Cook area I would follow the Tasman or similar and spot from the valley floor, locate animals, where they are feeding and look at how accessable they are, there will be some areas you wont want to go near with what the snows doing around now so a big long river with lots of glassing gives you more options.
I just came from Dunedin yesterday and there was lot of fresh snow in the Southern parts of tahr territory, from what I saw something a bit further north may be a better option
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