(Most tips by my friend Stefania, who is also an amazing artist!)
Courmayeur is probably the most famous Alpine resort in the Western Italian Alps, at the foot of Monte Bianco. It's two hours away from the airport of Milano Malpensa, very conveniently connected by a fast highway. If you go to Courmayeur in the winter though, I highly recommend you not to rent a car, because usually when there is a lot of snow and a lot of people for the ski "white" weeks (February is a popular month for that) driving tends to be very tricky, especially if you are not used to drive on the snow with chain tires - which is what most people use in Europe.
Therefore, if the hotel you book offers you a transfer from the airport, you should take it! And in Courmayeur there are many public buses that take you everywhere and to the ski trails.
There are many the activities you can do on the Italian Mont Blanc area in the winter... apart from the many ski trails (check the map, together with the near La Thuile sky area) I recommend also to go cross country one day, as it is particularly nice there, especially in the Val Ferret.
Another thing you absolutely have to do is climb to one of the Mont Blanc peaks (Punta Helbronner) with the new amazing Skyway gondola: https://montebianco.com/en/ , where you'll have the most incredible view on the Alps!
Check this website that has all kids of info: https://www.lovecourmayeur.com/
and this one: http://www.courmayeurmontblanc.it/
And read this nice guide that The Telegraph put together (this area is very popular with British tourists): https://www.telegraph.co.uk/travel/ski/resort-guides/italy/courmayeur/
In any case if you want to go to Chamonix (via the Mont Blanc tunnel, 70 euros) you can do it by bus or car (no train). People usually go there to ski only if there's not enough snow on the Italian side.
The FOOD in Valle d'Aosta is very traditional, rich and varied so check this out this guide before going: http://aosta-valley.co.uk/discover/food-wine/
Stefania helped me to compose a list of very good restaurants you should definitely try in Courmayeur (all to be booked well in advance):
- L'Auberge de la Maison (in Entrèves- 10 minutes from Courmayeur, also a lovely hotel) fabulous for the aperitif, dinner or after dinner!
- La Baita Hermitage (5 minutes above Courmayeur)
- Grand hotel Royal and Golf (also a fantastic hotel, in the heart of Courmayeur) very elegant and Michelin-starred (it also has a beautiful aperitif with firepits outside in the garden with oysters and champagne)
- Dandelion (10 minutes from Courmayeur), very traditional "mountain cuisine"
- Pizzeria Lo Sciatore Fuoripista, famous also for the grill (in Dolonne, 5 min from the village)
For lunch, on the cross-country track of Val Ferret (which also has a walkable trail, if you want to go without skis) Lavachey, with typical polenta dishes and game meat.
If you want to be really frivolous try also the restaurant on the slopes (they pick you up with the snowmobile)
Alla Grolla near Val Veny, on the cableway from Courmayeur to the Chaumiere of Plan Checrouit.