I was only there for a few weeks but in my opinion you have it right!
Staying in Aosta its a 15min cable car to Pila , Aosta has nothing to do with skiing , its a good sized town , genuine too as it had the Cogne factory which employed thousands.
So it has plenty to do! loads of shops and fantastic Roman heritage.
I dont think you would see it all in a week , if you go in late season you can be in shirt sleeves in the square drinking coffee and skiing powder up in Pila.
The resort of Pila i really liked , slopes are almost too perfect they are that well maintained , i never got bored lapping runs as you can take slight variations each time.
Plenty of blue runs and challenging technical runs from the top , one of them was fairly steep and narrow.
Very confidence building the entire resort and the blues are perfect for practice
Park is fun too for a variation of the main blue slope , couple of tiny jumps and rails for beginners which were a laugh.
Dont know too much about the off-piste but loads of bits you can take between pistes , esp off the very top.
Only gripe would be the main lift could be upgraded.
food and drink decent and sensibly priced.
Also worth mentioning the ski park for kids , didnt go myself but looks like it was for toddlers
That's really helpful @hawkwind, thank you very much!
That little snow park sounds really good as well - next year will obviously be too early for my little one to be on skis or a board, but I want to get him on snow (in some shape or form) as soon as possible!