Turin

Number of days depends on what interests you. Have you had a look at the various sites in Turin? Many palaces of the Savoys in the city and surrounding area, like La Venaria Reale, the National Museum of the Automobile, Cinema Museum, Egyptian Museum, etc. you can probably see two of those sites per day. Also a good city for just walking, shopping.

We like NH Hotels and there are several in Turin.

Two nights at least.

This is an excellent hotel and the prices are very reasonable.

https://grandhotelsitea.it/

I agree with everything that Laurel said and would add "eating" as another great thing to do in Turin. Also an excellent city for aperitivi, coffee, and chocolate.

Turin is chock-full of Art Nouveau architecture. I know I would need several extra days to see that.

I was there last year. Loved it. I stayed at the Grand Hotel Sitea (linked above) - which was great. How long depends on what you like to do.

Not a foodie, but food was terrific.

The OP no longer needs this info, but I thought I would add some thoughts on Turin. We just spent two days and nights there and would have spent three.

The people are fantastic. Everyone speaks English which is helpful and disappointing at the same time.

The city is full of history and architecture; take a few guided tours of the piazzas and buildings. Also, take one of the castle tours. We find that these sorts of sights are better with an engaging guide. Alex from WaysTours was excellent.

The market is huge! Worth a few hours.

The food scene happens at night, so you need more nights to check it out. We had a few excellent meals.

If we had more time we would have spread out our tours and walked in the parks and visited the sights (smaller castles and parks) outside the city (we hear that these are interesting). Also, the auto museum and Egyptian museum are excellent.

Routing - We flew into Geneva, took a mountain transfer to Chamonix, hiked for 4 days and got over jet lag, took a FlixBus to Aosta, rented a car, drove to Torino, and are now in La Morra (near Barolo). This is a good itinerary.

Lucky you in La Morra !! If you have time, try to have a meal at l'Osteria di Vignaiolo, in La Morra (frazione Sta Maria).

Our favorite restaurant in the area -- and my husband is a sommelier from Turin (I.e. he knows of which he speaks and isn't easy to please !)