Dunedin is a beautiful city and is a short 15 minute bus trip from Port Chalmers (where the ship docks). Unless you have a friend to take you on a private tour you should probably book a shore tour. Avoid the Cadbury Chocolate factory tour as I heard from people who took this tour that it's not that exciting and concentrates mainly on the packaging and advertising. Dunedin has the steepest street in the world and whilst I don't know about the veracity of that claim I can assure you that the street was very very very steep. The Botanical Gardens are beautiful and there is a lookout from which you can take amazing photos. Uniquely, Dunedin has an eclectic jewelry shop called Rockbourne Jewellery. The shop itself is located in an historic house and is extremely popular with Dunedin locals.
Christchurch: For Christchurch the port of Akaroa stands in and this beautiful port has amazing scenery. Located 1.5 hours east of Christchurch this little village was settled by the French and used to be a whaling port. This was the only tender port on the trip and I quite enjoyed the experience. For this port I did the 'Arthur's Pass Scenic Drive and Transalpine train ride. This tour was amazing, the scenery from the train windows is stunning and the last carriage is without glass in the windows so you can take photographs. The meal served onboard the train was excellent. Once the train ride is over (a couple of hours) you take the bus back to Akaroa stopping in at Homebush for afternoon tea. Homebush is an estate (working farm) that used to have a lovely big house that was unfortunately destroyed in an earthquake. The gardens are still there and are lovely, as is the homemade afternoon tea that was served; well worth the visit.
Auckland: The cruise ships dock right at the foot of the city and it's so easy to walk right into town. The views from the Sky Tower are impressive and well worth the visit. Auckland has some great shopping along High street and Vulcan Lane which are not far from Queen Street. For an amazing dining experience go to 'The Grove'. This restaurant delivers with impeccable service and amazing food. It really was fantastic.