A good alternative for the Kitzbüheler ski area is the nearby Wildkogel Arena. It is about a 10 minute drive by car to Bramberg or 20 minutes to Neukirchen. The area is a bit smaller than the Kitbüheler area and therefore less expensive. The area is perfect for families and beginners.
Some text from their website:
The Wildkogel Arena, our family-friendly ski area in the Hohe Tauern National Park Holiday Region, offers a magical snow-sports experience for beginners and experienced skiers on 62 km of beautifully groomed pistes. With the Wildkogelbahn lift in Neukirchen and the Smaragdbahn in Bramberg, you will be able to enjoy a comfortable ride up to 2100 m above sea level, where you will be greeted by glorious views of the 3,000-meter peaks of the Hohe Tauern range.
Once at the top - whether you prefer a more-laid back experience or an exciting high-speed adventure on skis, want to cut your own tracks through the deep-snow on your snowboard or set out on a ski tour through virgin nature - the Wildkogel Arena, in the heart of the Kitzbühel Alps, promises ideal conditions for a wide selection of winter sports. Due to a full range of difficulty, with slopes that are mainly rated "blue" or "red", the multiple-award-winning ski area on the Wildkogel is ideally suited for families, beginners and those returning to the sport after a bit of a hiatus. And for your added enjoyment, other extended ski areas, such as the Zillertal Arena and the Kitzbühel Alps - with around 300 kilometers of pistes in total - are also located close by. Likewise, winter hikers and sun worshipers also discover their own piece of heaven with us.
For additional information: