I was living in Christchurch last year and was looking for a place too shoot.
Unfortunately it seems rabbit number near chch are pretty low.
But if you want a place to just set some targets and have a blast you can go out to Lake Lyndon, there's a popular shooting area there.
I camped there one night and saw one bunny, but that was it.
I spent 10 months in Chch and did a lot of driving around Canterbury. I reckon I saw more bunnies on my drive home through the North Island, than the whole time I was down south.
That's not counting the ones that live at the Chch airport lol.
If I were you I'd try make friends with other hunters/shooters, and they will take you out.
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