I can't speak for Wellington and Christchurch as I have never lived there, but Auckland has some great outdoor attractions pretty close to the CBD.

Our family home is nestled in amongst the Waitakere Ranges in Cornwallis and while the website is probably a little optimistic about it being a 30min drive, it's still fairly close. 45min is probably closer to the mark

Waitakere Ranges

I would guess CHCH and Wellington would be even better than Aucks for this kinda stuff, but that's a guess.