not sure where to stay but i had an awesome days riding there. the descent from the chairlift to the river has to be the best trail i have ever ridden. La Thuile is only up the road and thats full of tekkie riding so take your A game there with no hangover.
I stayed in a small town La Rossier on the french boarder, took me about 1 hour + to get to Pila but a straight forward drive.
But cant praise Pila enough and cant wait to ride that trail again