Using FSET, you may in fact get full coverage of NZ, as I think this allows for different sources? I only use LINZ data, as it is distributable, but for your own use there may be a lot more available.
There is no reason why the entire Wellington region couldn't have a 2 metre mesh now, or even metre:) As I said, the data is available -- here's a screenshot of the LINZ Wellington 1m DEM coverage:
I think the only time I've used a 1 metre mesh is Kapiti Island. I'm not sure that it's worth the extra data, though... 5 metres is a good choice for large areas.