The skiing recommendations listed here starts with the biggest, most alpine area but then goes on to review some of the other complexes the town has to offer for all abilities.
Kasprowy Wierch Ski Website
This is the absolute BEST place to ski in Zakopane. It is alpine, located in two valleys fanning out from Kasprowy Wierch mountain which reaches an elevation of 1,987 metres. Since it is national park area, no snow cannons are allowed as they would disturb wildlife, so skiers must accept the snow conditions nature flings at them. This ski area, in lot of ways, is wonderfully undeveloped. I read somewhere that is is reminiscent of Austria at the end of the 19th century. However, that is not to say that it lacks the necessary uplift and infrastructure. Indeed, recent changes to how day passes operate has made this a super day out in some stunning scenery.
However, Kasprowy is only for intermediate and advanced skiers. Beginners, do not go here!