There is a pretty decent mall (with a Juve store

) in the Lingotto, that's right. There's also the Eataly store on the opposite side (a must visit if you're into foods & wines), but other than that, there's really nothing interesting in the neighbourhood.
Personally, I always stay in the vicinity of the Porta Nuova (main station). Very centrally located, and you can get to anywhere from there. The stadium is about a 25 min walk from here I think, but you can take the bus or tram as well (like many fans do).
Best hotel I've been to so far is the Atahotel Concord, but that can be quite expensive, depending on how/when you book. You can't go wrong with a Best Western either (there are about 6 or 7 in that part of town).
As for what to do, well that depends on you guys. Since I don't know what you're into: clubbing, museums, shopping, ...?