The closest thing that the Soviet Union had to convenience stores in cities would have been street kiosks. During the Soviet period t(which admittedly is a long time covering a wide range of policies), kiosks were basically outlets for local factories, or state owned monopolies. To that end they mostly sold beer, spirits or soft drinks, tobacco, flowers or ice cream - depending on the time or place there might be kiosks devoted to other sorts of items, but overall outside of a narrow range of permitted goods or services you would usually have to go to an actual market place, department store, state-owned store like a bakery, or one of the (occasionally permitted) small businesses like a hairdresser.

In 1992 kiosks were privatized and a massive explosion occurred in both the quantity of kiosks and the goods you could buy in them, especially foreign, imported items (Moscow was estimated to have some 19,000 by the late 1990s). The private kiosks have often had a love-hate relationship with urban citizens and authorities, most notably in Moscow, where a few years back there was a mass demolition. Nevertheless, they remain fairly ubiquitous in the post-Soviet landscape.