The Pah Homestead in Hillsborough is a historic home which is now home to a rather nice art gallery. The grounds with their stunning gardens and tree specimens are available for walking and you can take your geohound too. The home was built in the 1870s as a gentleman's residence by architect Thomas Mahoney. Prior to European settlement the site was home to a maori pa. Now the gardens are home to many exotic species including New Zealand's largest Moreton Bay Fig and hoop pine.
For this cache you are looking for something that arrived in New Zealand at the same time roughly as the home was being built. It was the first example of biological control of pests and if you have roses you will no doubt be pleased to have these around. See if you can see where it is having a rest.
Update: It's now a nano as someone stole the ladybird, which is a shame but there you go, people steal and that's why we can't have nice things.