Just got back from many of the areas you mention...you will have a lovely time.

Take care in the mountains due to the potential for snow as others have mentioned. Arthurs Pass is a somewhat small town but in the general area there are some decent clean places to stay. we used Trip Advisor to help us make our choices and were pretty pleased with the accommodations.

I also recommend a rental car for the Milford Sound excursion so that you can stop and enjoy the sights along the way. Milford very pretty and well worth the trip but Doubtful Sound is also worthy of consideration if you want something more exotic and "less travelled". Also watch the road conditions on your way to Milford here in winter months...can get dicey. If you intend to take a cruise on Milford Sound, you can book passage in Lake Te Anu at the iSight. Also plenty of places to stay in this small town.

We enjoyed Queenstown as well. The downtown was lively and there is lots to do in the general area.