As far as I know, suburbs are the area outside of city's limit, but is urban, and several people live there. As an example, the parts which are counted in New York's urban area, but are not one of the 5 boroughs, like some of the areas east of Queens and Brooklyn on the Long Island.
Nice work Gassu. For your reference, there is a recently released data source for NZ localities which should interest you. In cities, it is generally representing 'suburbs': https://data.linz.govt.nz/layer/104830-fire-and-emergency-nz-localities/
This is probably the quiz which took the longest to make in comparison to the number of people who took it. Great map, but I'm just not an expert on Auckland. XD
These aren't exactly suburbs-some may be outside the purview of the central city, but the CBD and the area around that aren't suburbs-they are directly part of the city. Maybe a better title would be districts/neighborhoods of Auckland?