I ride in Pila a lot (I live couple of hours away) but as per previous poster it is predominantly a downhill/freeride resort. La Thuile has more chilled trails but also mostly lift accessed. There is a famous (but tough) big XC route in the Parco Gran Paradiso which is on the southern side of the Aosta valley, accessed from a lovely little ski resort called Champorcher. It is a multiple day circuit and probably requires too much planning, but Champorcher would be a good base to do some exploring incorporating some of the route.
This is the overview on an italian MTB forum (in italian but good pics):
http://www.mtb-forum.it/community/forum/showthread.php?t=47525
Map (Champorcher is top right):
http://www.mtb-forum.it/bike/granpa/bilder/cartina.JPG
Parco Gran Paradiso is truly a stunning part of the Alps.
If you need any help with italian happy to help
Ben