In reply to DaveHK:
There's some side-piste and slackcountry in La Thuile itself, but there is also a tour that starts in Courmayeur and ends in La Thuile. Didn't end up doing it when we were there, but easy to work out on the map. You get 2 days at Courmayeur on the La Thuile lift pass and the bus service is great.