Split Enz & Crowded House as one band, but I'll also include the Flight of Conchords as a band (which I admit is debatable). The third, and surely deserving of your attention, is Auckland's The Naked and Famous (TNAF). The local alt-rock station (96.1) started playing "Young Blood" in high rotation over a year ago and after poking around on Youtube, I decided to buy their 2010 debut LP "Passive Me, Aggressive You".
My iTunes play counts don't lie: I really like this LP. I recall on the first listen, on every track I recounted the various moody, 70s & 80s synth pop influences (e.g., Roxy Music, Joy Division/New Order, Depeche Mode) but there were so many that I eventually decided if you incorporate dozens of different influences and update them by 20+ years then you've really created something new. Another thing they offer is they rock a lot harder than any of their influences -- they must have every distortion pedal that exists in New Zealand. The other distinguishing characteristic of the band is that Aaron Philip Short & Alisa Xayalith work the shared, male/female lead vocals to perfection.
I recently I bought their first two EPs and while not bad, they don't give any hint of how well this LP would come together. Their next LP, "In Rolling Waves", is due in less than a month and the advance single ("Hearts Like Ours") is already out. We'll see if they can catch lightning in a bottle twice.
Standout songs: "All Of This" (live version), "Punching In A Dream", "Young Blood" (live version), "Girls Like You" (live version), "The Sun"* (live version), "Jilted Lovers", "No Way"
Skip 'em songs: "Eyes" (they carry the John Hughes soundtrack influence too far here...)
Final score: 9/10
Bonus link: lots of good stuff on their Youtube channel
*="The Sun" makes it clear that their LP collection contains "Kid A" too.