Skiing is still very much the king in Austria, but you see some boarders on the pistes. Here's where I've skied in Austria:
Lech am Arlberg: Isolated and rather expensive but very nice resort in the far west of the country. It's at a fairly high altitude and it tends to open slightly earlier than other resorts. There aren't really any major cities nearby. Closest is either Innsbruck or maybe even Zürich. I don't think it has a terrain park.
Kitzbühl: One of the largest winter resorts in Europe, with plenty of slopes for all levels. Lower in altitude, so it may open a bit later and generally closes earlier. Lots of good nightlife, but bring some nice clothes. Münich, Salzburg and Innsbruck aren't too far away.
Obertauern: High altitude purpose-built ski resort, as opposed to a pre-existing town that evolved into a ski-mecca. Cheaper than the two other options I've listed. Closest to Salzburg and Klagenfurt.
If the early winter is especially warm or dry and the resorts are having trouble accumulating enough snow, look into Ischgl and Hintertux. I have not visited either of these resorts, but the upper slopes are permanent glaciers. At least one year that I lived here, Hintertux opened for the season as early as late September.