My usual caveats are that it will depend on the time and place (80+ years in the largest country on earth, after all), but if you are looking for social histories of the USSR with a focus on Russia, then Sheila Fitzpatrick's Everyday Stalinism and Stalin's Peasants are probably the best place to start.

The former in particular covers social life in urban Russia during the 1930s, is relatively short but is jam-packed with details, and is probably Fitzpatrick's best-known and most-cited work, at least after her Russian Revolution history.

For anything after the Stalin period (post 1953), there aren't as many straight-up social histories. Svetlana Alexievich is useful and insightful, in particular her Zinky Boys, but she is a journalist and essayist rather than an academic historian.