Lillehammer is the oldest ski resort in Norway and you will find lot of skiers from all over the world there. Most of the alpine skiers travel to Hafjell, 15km north of town. At Hafjell there is plenty of ski in/ski out accommodation og hotels.
If you like the nordic way of skiing then take one of the local coach to Nordseter or Sjusjoen. This area have almost 300 km with ski tracks and is a winter wonderland.