I'm not an experienced skier, so I've tried to rate Åre in relation to my own experience there and in relation to what I've read about other resorts. It'd be great to see reviews from others who have traveled more extensively.
I spent a week in Åre last year — my first-ever week of skiing — and had an amazing time. I went with a group of intermediate skiers and, between the lessons I took every morning and their encouragement, I was mostly able to keep up with them by the middle of the week.
It's familiy-friendly, but Åre is also known for its nightlife. Everyone speaks fantastic English. Lots of varied terrain, and easy to get around.
It is not expensive to stay there. I shared a good-sized ski-in/ski-out cabin literally right on one of the main slopes with 5 other people for a week, and price per person was 1000 SEK (~ $140 USD).
I list its size as a con, but really I don't think it's much of one. There's plenty of a week of skiing, and if you find it lacking, there's plenty of offpiste terrain (guided or unguided).