The State Departement Store is situated on Peace Avenue. You cannot miss it. On the ground floor you find a supermarket. On the top floor you find all the locally produced souvenirs and also batteries. Among the wide range of souvenirs you are bound to find something that catches your eye and the prices are fixed.Somewhere on another floor there is quite a good little music shop where you can find CDs and DVDs from Mongolian artists.BTW, the State Department Store has nothing to do with the state anymore. It's a left-over from the Soviet time.
The is called black market is located outside the city center. Nowadays it's called: Naran Tuul khudaldaany Tov.
Almost all of kinds of food products and other goods are sold here. It operates during the whole year. If you have time, you can buy everything you want here at the market.