In reply to BHound:
As a beginner you don't have to go to one of the big resorts with 100s of kilometers of runs, because you will be paying for something you don't need. Small Austrian resorts can be very friendly and a nice atmosphere for apres ski relaxation, because as a beginner you will get very tired and need to unwind, although not to the extent that you miss ski lessons the next day!
It's important to choose an instructor who speaks fluent easy to understand English as it's much better for you to learn the techniques from someone you can understand and converse with easily. This where America would be a good choice. Also the Americans are much better at policing the pistes so that you don't get intimidated by faster skiers coming by close to you. Some Continental resorts get overcrowded with too many out of control people all over the place which often worries beginners.
A couple of sessions at a dry ski slope before you go is worth considering as it will get you used to the concept of you feet sliding away under you and you staying over them!!
Be prepared to fall a bit to start with but you will get the hang of it very quickly. If you get in with a nice group of fellow beginners it can be quite a laugh. I've been skiing for over 60 years and metamorphosed from 2 meter plus wooden skis with fixed cable bindings to modern carvers and release bindings, but I still look back on my first week as having been the one of the best fun wise
Good luck