In Italy shopping for food is not too expensive, especially if you go to local open air markets, where you can find any sort of fruits and vegetables, dairy products, meat and fish, as well as clothing and sometimes kitchenware and house accessories.
In the area surrounding IST, there are several farmer's markets where you can go buy fruits and vegetables, as well as meat and cheese, directly from the farmer with good prices for excellent quality.
There are obviously many supermarkets around town. The main chains are:
Carrefour
Coop
Pam
Crai
Borello
Lidl
Penny Market
Mercatò
A&O
Basko
There are also bigger shopping centres in Turin and around town, where you can normally find not only supermarkets but also restaurants, clothing, jewellery, shoes, IT, beauty products, etc.
Just to give you a couple of names, you have Le Gru and 8 Gallery (where you also find Eataly, the best of the best of Italian food and beverages, and now Green Pea a brand new environmentally friendly shopping venue)
In Turin, people love walking around after work or at week-ends, to go shopping (or window-shopping only!). In downtown Turin, you will also find some of the main brands of clothing stores such as Zara, H&M, Mango, Benetton as well as a good selection of high end designer stores.
Restaurants:.....you only have to pick one. Turin is the capital of fine eating and drinking.
Food delivery: Foodora, Just Eat, Deliveroo, Uber Eats, then pizza take aways at every corner!
Some useful links for you:
https://www.tripadvisor.co.nz/Attractions-g187851-Activities-c36-Piedmont.html
http://www.browsingitaly.com/piedmont/piedmont-cuisine-7-dishes-try-northern-italy/4857/
https://www.independent.co.uk/travel/europe/piedmont-taste-of-the-north-480807.html
http://slowitaly.yourguidetoitaly.com/popular-foods-of-italy/
http://www.comune.torino.it/torinoplus/english/viveretorino/mercati/mercatimercatini/index.shtml