There are plenty of food markets with fresh produce and other goods. Many smaller shops in Mongolia still don't have a supermarket style experience and you are forced to point and ask for goods from the shopkeeper. However many larger stores are supermarkets and have western goods also. The larger shopping centers with good supermarkets are located in Sky Mall (near the Chinggis Hotel), the food section in the State Department Store, Nomin super/hyper markets, and others.