We sailed earlier this year on the Stadenham and visited Tauranga, Wellington, Christchurch, Dunedin, fiordland, hobart (cancelled due to rough sea)2 days in Melbourne and then Sydney.
Tauranga if you like wildlife i reccommend the wildlife/maori tour. It is very interesting and we organised this through the ship.
Wellington - DIY. A group of 8 of us caught the yellow circle busses (every 20mins) 3 or 4NZD hop on/hop off. This is excellent and lets you see everything at your pace - Te papa museum is a highlight. The maratime museum is interesting as is parliment house.
Christchurch- Tranz alpine train trip - absolutley fantastic journey into the southern alps. Scenery to die for. Must do.
Dunedin - We booked ahead with back to nature tours. This is the scottish city of NZ and it was fitting our guide Chris had a scots accent. He was charming and knowledgable on the wildlife as they specialize in wildlife tours on penguins and albatross. We managed to fit a lot in the day at a relaxed pace - I highly recommend Lanarch Castle because of the wonderful gardens and make sure when you book your tour you get a city tour because the archeticture and viewpoints in this city are great. Highly recommended A+++++
Fiordland - the scenery here is unlike anyting you could imagine. Mountains up to 1600m rise from the sea. It rains a lot there (2 out of 3 days) so be prepared for low visibility.
Melbourne - If you enjoy a coffee go to Lygon street. The transport in this city is great. A free pass for the trams,trains and busses is only $5ausd for unlimitted travel. We just got lost in this city and discovered a lot of stuff we'd never even thought of. The Victoria Markets was great.
I hope this gives you an idea of some of things you could do...happy cruisin