places to not miss in Austria?

You do realise there should be heaps of snow on the ground, so although you might go X-country skiing, a nice hike in the forest could be out of the question!!   And further, in that short time, you need to concentrate on your skiing - a week is no time to be thinking about visiting other places.    I'd say a day on the slopes would be more than enough for anybody's energy level.    Save your sight-seeing for another time, perhaps in Summer when you'll be able to get around more easily.

At first thought Hallstatt, but the whole of Austria was blessed with perfect beauty !!!!!

With only a week and one of those Christmas, four places is plenty to try and cover especially with Christmas mixed in. Vienna and Salzburg both have a lot to see and do.

That sounds like you're doing too much - I'd stick to the slopes, plus the apres ski

I would advise googling migrant rape in Austria before going