What dates are the cruise that you are on? I grew up in Tasmania and work in the industry so I can definitely help you out with some of your questions? Here is a little bit about what I know and then let me know if you do have any other questions.
Hobart (my home town) - is great for sightseeing and the port is very well set up for passengers with free shuttles into town and back to the ship. Hobart, especially Salamanca Place is beautiful and does some amazing souvenirs, arts and crafts!
If you elect to do a tour Hobart and surrounds is very picturesque and lot of beautiful natural scenery. Port Arthur is extremely well know for its fascinating history and past, but it is a bit of a drive and can get quite crowded, especially when a ship is in. Some amazing alternatives are Tahune Airwalk, Richmond Village, Russell Falls and Bonorong Wildlife (will mean you can see the Tassie Devil), Mt Wellington, winery tours etc - there are lots of options. If you are interested in organising a private tour or booking with an independent tour operator I can also provide you with some great information for Hobart. I am currently setting up a website Shoretours.com.au which allows cruise ship passengers to help find local operators and if you would like I can send you a brochure.
The other port I know a lot about is Sydney, its where I live now and I think its one of the most beautiful cities in the world! I hope that you are able to spend at least a few days here, Bondi Beach, Opera House, Circular Quay, Blue Mountains Hunter Valley are all beautiful and different to what you will see in the other ports.
Weather wise - I am sorry to break the news to you but you will need to pack for all 4 seasons! Sydney has been incredibly hot already this season - we have already had 41C this year! And Hobart and NZ are quite a big farther south so I would still recommend pants, jeans, light sweaters and a jacket. Please do not forget your sunscreen! We are not kidding when we talk about the Australian sun, even for Hobart.
Like I said, if I can help with anything else let me know, else enjoy your cruise, you are coming to a beautiful part of the world!