Correct. You can stay up to 3 months without a visa.

It'll be a good time to travel I guess. Summer time has longer daylight hours, can do more stuffs. Daylight saving times usually start ends September and finishes early April.

Not sure if there is any wineyard in between your journey, as we are coming from north to south we will be visiting vineyards around Picton.

My schedule excluding North for your reference (Slightly different as we had to cover North for some reason)

Day 1:
Morning - Ferry from Wellington - Picton
Afternoon - Vineyard
Drive to kaikoura for a night stay

Day 2:
Morning - Whale watching
Once done will drive to Christchurch to explore the town area / Akaroa if we want to
Overnight at Christchurch

Day 3:
Lake Tekapo / Pukaku / Mt Cook
Overnight Queenstown

Day 4:
Milford Sound
Overnight Queenstown

Day 5:
Morning explore Queenstown
Afternoon flight to Auckland

Day 1 (11th Nov)
You drive? If so, put some time in Arthur's Pass. Not much to do in Greymouth, I suggest you skip.
For the Glacier, you can only view it from afar unless you join a tour. Btw, that's a lot to do in just 1 day!

Day 2 (12th Nov)
If you join a tour (min 4 hours), you still want to drive all the way ? ... Good Luck!

Day 3 (13th Nov)
Day 4 (14th Nov)

Day 5 (15th Nov)
Why return to Queenstown? Just stay overnight in Dunedin, lots to do/visit there! Or you can overnight in Oamaru for the blue penguin colony

Day 6 (16th Nov)
Cromwell in Spring? Skip it, spend your time in Mt. Cook!

Day 7 (17th Nov)
Another whole day of driving ... Good Luck!

Day 8 (18th Nov)

The half day glacier tour, you need to join in a tour to walk up the glacier.

Remember there's an accident happen like 2 years ago (See here)? It's dangerous to walk near a glacier because it's constantly melting and breaking. If you don't want to join a tour, you can only view it from afar.

Day 1
Nothing in Greymouth can skip. If you have time, spend a short while in Arthurs Pass to Devil Puchbowl waterfall. Very nice.
If you don't have enough time, suggest you to stay overnight at Fox glacier instead. It's take shorter time and route to walk from trailhead to the glacier face compared to Franz Joseph, if you must see glacier. And at Fox glacier, you can have a walk at Lake Matheson.

Day 2
On the way from west coast to Wanaka, u can stop by Lake Hawea. mirror like lake wif weather is good. There's a rippon vineyard at wanaka but how much is the cellar door visit i have no idea.

Day 4
2 places in a day, not sure enough time or not as they are in different direction. suggest to stop by kawarau bridge to see ppl doing bungy jump on your way to arrowtown.

Day 5
Dunedine - Speight's Brewery tour. drink kau kau, only if u stay overnight
I remember when i was on road trip from oamaru to questown, we stopped by aviemore dam. i just like the place and at cromwell, lake dunstan. just awesome to have that kinda view on a long road trip...

Day 6
The salmon farm is on the way from mt cook to lake tekapo route

Day 7
Suggest you to vist the seal pups at kaikoura. super cute.
have fun!

Are you going for glacier hike? To me, i think your day 1 & 2 just driving. lol. if you're not going for a glacier hike, just skip west coast lah. you must join a tour to step on glacier, else just see from far. then you have more time to spend at queenstown or go to oamaru like suggestion by fallout.

btw,w not doing skydiving? 

Please do comment and help on the itinerary.

Day 1(Thursday)
Christchurch - Lake Tekapo
Day 2(Friday)
Lake Tekapo - Wanaka - Queenstown
Day 3(Saturday)
Queenstown - Te Anau - Milford Sound - Queenstown
Day 4(Sunday)
Queenstown - Arrowtown - Queenstown
Day 5(Monday)
Queenstown - Glenorchy - Queenstown
Day 6(Tuesday)
Queenstown - Melbourne 

As it just gonna be a short trip, so I prefer something more relax and less driving hours. Anything I can add or change on the locations?
Do I need to book advance for the Milford and Glenorchy cruise tour? Any recommendations on the company? Thank you!