Archives NZ is a great place to find titbits of information.
They hold schools rolls so you can see what schools your grandparents / great grandparents attended. They also have old school photographs.
The Auckland branch also has the Gum Diggers records, so if any of your whanau were gum diggers you can find when they worked, who with and how much they got paid. Often you will find that those that they worked with are relations.
Archives NZ also hold some of the Maori Land Court Records.
Anyone can visit the Archives NZ. You fill out a request to be a researcher and then the staff will show you how to access the records. They are very helpful.