Some good advice so far......
Air New Zealand fly from San Francisco to AKL, or you could fly direct LAX to Christchurch. Flying direct to CHC saves you the hassle of getting connections and losing travel time getting from AKL to CHC. A lot of the holiday promotions at our end are for 'Air Canada'
I may be biased but I'd suggest skipping the North Island and spending all your time in the South Isalnd. Christchurch is the major base for rental car firms and most have ski deals - Hertz, Budget and Avis. Not sure what sort of deals you'd get in Queenstown, but you can pick up rentals there. If you fly into CHC it is a beautiful drive to Queenstown and you drive by several so ski areas on the way.
I'd suggest getting a 4WD or AWD - you can rent Subaru's here, which make great ski vehicles in NZ. Most of the time you won't be travelling on snowy roads except the last 10kms or so on the ski area access roads. You don't want the hassle of fitting chains. Even with 4WD they make you carry chains cause if a storm comes in and the orad ices up, you need the chains to get down. Because most of the access roads are across barren mountainsides there are big drop offs, so it pays to follow the rules.
With a group of 6 or so, you probably need to plan ahead for accomodation. In NZ, motels generally have kitchens which can save a bit making your own breakfasts etc, plus you don't waste time in the morning going to a restuarent. Many motels also have family units, eg. two bedrooms, so can make it quite reasonable when you have a group.
Another option, is to rent holiday homes through real estate agencies, ideal for a group. Some require you to take your own sheets and towels but I am sure they have linen packages for a fee. I'll hunt out some web sites for you.
Many skiers rent campervans, which are fine in our climate, cause you are sleepoing below the snow line. They are slow getting up the access roads, but heaps of people do it so can't be that bad. All our camping grounds cater for camper vans, there are thousands on our roads.
Skiing in NZ is quite different to North America. No trees, and when you are not skiing you are below the tree line. You can visit vineyards, or even go mountain biking if you want.
If you want to search on the web within NZ, go to www.google.co.nz
and only search within NZ pages.