Hey - it looks like you are getting some quite good info but I thought I would add in my 10c worth. My home field is Mount Ruapehu in NZ's North Island but I learnt to ride in the South and ride there as often as I can so I offer some unbiased advice.
You cannot beat Queenstown for location and lack of distance to a variety of good commercial fields (20 - 40 mins on a bus from accommodation to hill. Good night scene, great restuarants and really is New Zealand's adventure tourism capital, i.e. bungy, white water, jet boating, paragliding etc etc. Downside is it is comparatively expensive to elsewhere in NZ but if you are coming from overseas the exchange rate should work in your favour.
Wanaka is also a gorgeous location. It is smaller and more laid back than Queenstown and has less of a night club scene. Still has fab restaurants/bars and you can do most of the same sort of adventure tourist activities as you can in Wanaka. It is only about 1.5hrs drive from Queenstown.
If you only have a week - I would base myslef at one of these towns.
Cardrona (closest to Wanaka but accessible from Queestown - about an hour to hours and a half drive) is best for park/pipe and has a good range of really open green and blue runs. It is however, less interesting for anyone who is up to riding blacks. They were also doing a fab breakfast of porridge, cream and irish whisky last time I was there
Coronet Peak (closest field to Queenstown) is the field that feels the most commerical or touristy to me - really good rentals if needed by your group however. Lift lines drove me nuts last time I was there though
This is important in NZ as runs tend to be shortish when compared to overseas so you spend a lot of time admiring the view from the lifts or standing in line. It also has a goodish park. If, however, you can only ride one mountain and your group is of mixed experience - then go here as it has the best range of runs of various levels.
Treble Cone (Wanaka is closest town) is really good if your group is more intermediate to advanced - steeper longer runs and more interesting natural terrain. Not too good if anyone is restricted to greens as there is not many of those. Along with Cardrona this is one of my favourites!
Snow Park is also pretty awesome. If any of your group is into park they should give this a go - massive purpose built terrain park just outside Wanaka. Huge selection of pipes, rails, hits, and jumps.
The one field I cannot offer any insight on is Remarkables as I have never been there
As far as I know there is not anything like a ski only multi-pass that covers all the fields apart from a seasons pass for Hutt, Coronet and Remarkables (all owned by the same operator). The closest thing I have heard of is the NZ Superpass NZ Super Pass
which appears to be some sotr of activitiy/ski pass rolled into one.