You can't go past the Auckland Art Gallery here. While their website is starting to look a bit geriatric, I think the online collection and the digitised resources are the best in NZ.
Word on the digitisation grapevine is that the AAG will be releasing a new digital product next year, which will add wiki-style commenting to a heritage resource.
Also worthy of mention:
Christchurch Art Gallery with their growing collection of Audio on Demand.
Te Papa's new mini-exhibition sites are nice to look at, and the Zoomify is cute. At the moment though there's no sectional nav (not even breadcrumbs) and you can get foisted out unexpectedly into TP's main site, which is a bit disconcerting. And this leaves me wordless.