There isn't much in Big Sky to see. Shopping, forget it! But there is this great little market that is worth the visit. Touts a big wine and beer selection, amazing selection of groceries including meat, produce, spices, chocolate, etc! Prices aren't cheap but not outrageous either.
It's called the Mountain Mall but it's equivalent to the size of a strip mall on a street corner. About 3 gift shops, a sporting goods store, a Starbucks, a couple of restaurants, a small market/convenience store, a very nice (really) fur coat shop and on the second floor a large cafeteria type area and a business center.
It's adjacent to the ski lift and in between two hotels/lodges.
Shops include the Hungry Moose market, Blue Moon Bakery, The Lone Perk, Trailhead Pizza, Big Horn Boutique, Grizzly Outfitters, Choppers and a few others.
Not a big shopping center. The Meadow Village looked like it may had a few more shops. The Skyline Bus will take you there.