If you had the opportunity to go anywhere in the world to ski,
Heh, I spent almost $20K for a 3 week ski trip to Lyngen and Svalbard :)
I had the money and I wanted a trip of a lifetime, so that is where I went! (It actually cost me less than $15K)
But since the OP is from Norway already, flying to Troms or Bodo is a quick hop to get to world class steeps and one can rent a camper van to stretch out a 3 week trip for not so much money.
I'd therefore suggest something which is much different than the Arctic alpine terrain of Norway ... Skiing pillow fields and old growth forests in British Columbia would be quite different from the treeless terrain in Norway. Of course, some would say that Lake Tahoe actually has the most legendary tree skiing in the world, due to how well the trees space out as the forests age and burn ... But the vertical isn't so great and the steeps aren't as sustained as other mountain ranges. Still, for $20K you could probably fly to US or Canada and buy yourself a sled, as you will get way more laps sled shuttling with a buddy than via awfully slow snowcats. I haven't been watching the Kroner but I bet it goes a long ways in Canada right now???
If you had the opportunity to go anywhere in the world to ski,
I was talking to friend last night who just got back from 3 weeks in the alps...I think that's where I would go