Hi Jack,
Definitely April - the weather is usually quite settled and calm although some frosty mornings can be expected. September (spring) is usually windy, wet, and can be cold.
The link for forums & maps are above and I have to agree more time spent in the South Isl is better even though I live in Auckland!
Please feel free to get in touch if you need more detailed info or would like to meet up with some local cachers when you get here.
Alan/GreenBLAT