If you're looking for administrative (legal) boundaries, then they are published by Statistics New Zealand and you can easily download them from Koordinates:
There are regional council boundaries, territorial authority boundaries, ward boundaries and community boards, which are all legal boundaries of local government. There are general and Maori electorates for central government elections. There are also non-legal statistical area boundaries, like area units, urban areas, and meshblocks.
There's no official legal definition of a city's boundaries, or in most cases, of the suburbs within a city. The only councils with officially defined suburbs are
Wellington City: http://koordinates.com/layer/1431-wellington-city-suburbs/
Porirua City: http://koordinates.com/layer/6073-pcc-suburbs/
The former North Shore City also had official suburbs, but that council no longer exists and I couldn't find GIS data for them online.
The closest thing to a national suburb set is the "NZ Localities" dataset maintained by the NZ Fire Service http://www.fire.org.nz/ and while it is free (as in beer) you will need to agree to a licence agreement to use it: http://officialinfo.wordpress.com/2009/04/17/response-from-the-fire-service/