In reply to Oo:
Having skied in Lyngen, Lofoten, Møre og Romsdal, Sunnmøre, Sogndal, Hurrungane, Jotunheimen, and a few places in between, they all offer world class ski touring, but Norwegian weather is pretty harsh, and it can be difficult making good calls with regards conditions. You need to be avalanche aware.
Weather forecasts are sketchy, so it's often worth trying, as you can always turn back. You might get a brief break in the clouds for a spectacular view. My first trip to Lyngen we kept turning back 30 minutes too soon, getting down to see the peak basking in sunlight, although it's difficult to keep going when it's windy cold, and you can't see a thing!
As others have said, hut to hut alpine touring isn't so common, with the Jotunheimen haute route an exception (
http://xn--hgrutajotunheimen-00b.no/en/ ). Also, Patchellhytta in Sunnmøre has some incredible peaks nearby.
I can't think of any other cabins that are worthwhile staying in rather than renting a holiday house.
The Fry Flytt books are excellent , and a fair few come in English. ut.no has the Norwegian equivalent of ordnance survey maps online, with lots of tours, huts, and general useful stuff described.
This is a good resource for finding holiday homes:
https://www.finn.no/reise/feriehus-hytteutleie/resultat?redirect=mfinn
The best week I've had was in Sunnmøre, staying at Standalhytta - it's most likely sold out for Easter, but you could try. It has some great tours straight from the hut, and then there's a whole bunch of incredible tours within an hour drive.
Lyngen is also incredible, I had a great week last May skiing many of the classic couloirs and also the Jiehkkevarri traverse. Search for
Isfjorden in Romsdal has a whole bunch of excellent skiing, with Kirketaket a Norwegian classic. I've often stayed at Åndalsnes Camping - great value. Kilian Jornet lives in the area and his Facebook feed is full of epic pictures and videos. Watch from 7:00 here and tell me that isn't one of the most amazingly beautiful lines you've ever seen!
http://runningmagazine.ca/video-kilian-jornet-runs-and-skis-77k-seven-summi...
Lofoten is great too, but I didn't have the best conditions to enjoy it when I was there. The conditions may not be so good by mid April. I had to drive a lot to find stuff, but the scenery is great.
I've rarely had great conditions in Sogndal, Hurrungane or Jotunheimen, but I've still had some great ski days.
Have a great trip, and hopefully the conditions are good.