alps are renowned for its off-piste area. Verbier is probably the #1 resort for off-piste.
courcheval/3 valleys is also good if you get along well with obnoxious new money siberians.
although the french side is very nice i prefer verbier/zermatt/saas fee even though the swiss' french accents can get pretty weird.
verbier is very nice because almost everyone speaks english, it has a lot of English, meaning great britain, tourists so it wont feel as foreign. Also everyone, and I mean everyone goes in for tea/coffee time at 10-11 and again at 3-4 so you really can get some quality ski time with no lift lines in during the day no matter how crowded it gets during the holiday times.
austria has st anton which is the best in austria, nice if you know some german, and has less of an "older/mature" crowd, more younger people in the town which makes the apres ski very lively.
All in all, I love the alps and I stay here almost every winter I can because almost all the resorts are part of a community of resorts, usually some number + valley, kind of like lake tahoe, but they are all interconnected by lifts or trams. This means you can get some really extensive skiing done without every skiing the same run twice if you dont want.
The alps also get very nice dry powder and most of the slopes are higher in altitude than anywhere in north america so it just results in very quality snow and skiing and weather conditions. Rain? never during the season.
Also the alps has a very lower percentage rate of gapers than north america. even the nuclear family of mom dad, 2 little kids all know how to ski parallel, get on the lifts, not crowd the start of runs, and wont point at your skis and call them twin tippers.
Bring your powder skis, the alps resorts are the biggest in the world and there is virgin powder for days after a dump.
Originally Posted by bob4snow
Common misconception that know one skis off piste in Europe. Reality, almost everything other then marked trails are off piste and since they are so expansive you usually don't see anyone. We American are so use to the homogenized marked trails that everyone spills onto.
As for your question, a lot depends on how you want to stay and ski. Ski in - ski out? My personal preference after living in Europe for 6 years is Lech, St. Anton. Although I could suggest another dozen resorts that all offer something a little different, these offer easy access to the lifts, a great intimate town and great skiing. Frankly, my wife (from France) would suggest just about everywhere over there.
Your other choice in France, Verbier/4 Vallees, are wonderful as well. But you could also look south to Cortina.
Good Luck choosing.