You might want to look at either Woosh.co.
nz or telecom.co.
nz (Jetstream) or I think there is a couple o companies that provide wireless or cable connections for Wellington.
As per
http://www2.paradise.net.nz/plans/highspeed.html :
Cable
Paradise.net cable connections are available to people living in cable connectable areas in Wellington and Christchurch.
To check residential plans, pricing and availability, call 0800 299300 or visit TelstraClear.
Paradise ADSL
The paradise.net ADSL plan allows access via TelstraClear's High Speed Internet (ADSL). Click through to TelstraClear to find out more.
Citylink
Citylink is the fibre optic network that connects much of the Wellington central business district and allows high speed internet access at either 10 megabits or 100 megabits per second.
Because Citylink is not available in other cities, the paradise.net Citylink plan is only available to Wellington customers. Wellington customers who are not in the CBD can connect to Citylink by way of a TelstraClear Cable Modem and surf at speeds of up to 2 megabits per second."