My husband and I will be travelling to NZ for a total of 10 days (fly out on day 10) in early November. I have started my research recently, but would like to get some idea on what cities/areas are a must-see and what can be skipped.

Given the country's landscape, I would incline towards nature activities, but would like to get a bit of a feel for it's culture too. After seeing the distances, I am open to flying between the NI and SI as well as maybe flying into NI and flying out of SI. If possible, I would like to keep a day free to relax on a a nice,warm beach towards the end of the trip, but not sure about how warm it will be in Nov.

Thanks in advance for your help and suggestions.

With only 10 days, I strongly suggest you stick to one island, and I recommend the south. Drive distances in NZ are much longer than they appear on a map. Roads are narrow and winding and and it can take a long time to get from point A to point B. The terrain is rugged and some routes aren't as direct as you'd think due to mountain ranges, etc.

In your time frame you could do something like this:

Christchurch-Arthus Pass-West Coast (glaciers)-Wanaka-Te Anau-Milford-Queentown-then fly from QT back to Christchurch for departure.

Or you could do Christchurch-Lake Takapo-Mt Cook-Wanaka-Te Anau-Milford Sound-QT - then fly back to Christchurch

Or you could do them in reverse, fly to QT first then work your way back to Christchurch via car.

The main differece is the routing - you must choose between the west coast route (glaciers) or the inland route (Tekapo-Mt Cook). I'm partial to the West Coast route, which I think is absolutely stunning, but it takes a bit longer.

Both routes enable you to see some of the most popular attractions and some pretty incredible scenery.

White Island by Helicopter. It is an active volcano off the north coast.

Here is spectacular as well.
http://www.waimangu.co.nz/

I thought Wai-o-tapu near Rotorua was must see. I think you could do both islands in 10 days if you plan carefully, although you'll probably have to fly between the islands at some point because it actually is further than you imagine. I also preferred the North Island, so I disagree with Melnq8 about only doing the South.

It is hard to pick must sees. This is complicated by November weather which is still subject to late spring southern storms which can completely wash out a west coast leg. If you've seen glaciers elsewhere you may not want to do the west coast, and Arthur's Pass is definitely toward the bottom of the must see listing.

For a first visit many people do like a visit to Rotorua/Taupo area for a combinations of the culture/geyser/volcano scenery (and it is conveniently close to Auckland). You can also fly Rotorua to the South Island, Christchurch in particular has excellent fares. You may want to book these without much delay on Air New Zealand (look for the grab a seat fares).

From Christchurch you can rent a car and drive either down the east or west side of the Southern Alps, to Queenstown and spend the balance of your time in that area, including the trip to Milford Sound. I happen to prefer the scenery on the east side (Mt. Cook, the turquoise lakes and the tussock country).