Having driven into Wellington the day before, we went off to the "Te Papa" museum.  Being a motorcycle fan, I was drawn to the Britten race bike on display.
In the afternoon, we ascended the mountain which Wellington is nestled against, via the cable car.  One good thing about it is that the cable car still serves as public transport, so you pay $2.50 for a return trip on it, as opposed to a completely inflated price for it being a tourist haunt.
There's also a small cable car museum at the top, for the tourists to relive the highlights of their recent journey.