Andrei Makine has written some rather impressionistic works, one of which, Once Upon the River Love, won the Prix Goncourt and Prix Medicis. It's also non-Moscow, non-St Petersburg, being set in Siberia. It's a bit of a memoir, based on his (I think) grandmother's life. He wrote another, The Crime of Olga Arbyelina, which is a bit more emigre in setting, but he manages that beautifully as well.
More modern stuff: do you read French? Gilles Leroi wrote an incredibly beautiful book about Leningrad/St Petersburg, covering the latter part of the 20th Century. I think it was L'Amant Russe. However, if you have any hang-ups about homosexuality, it might not be for you!
Boris Akunin's Fandorin series is an absolutely brilliant evocation of the late Tsarist period, but has clearly modern preoccupations (what is Russia? Is she in Europe? Is repression good, or is self-discipline the only worthwhile kind of repression?)
WRT the French, a lot of classic stuff, and particularly emigre literature is translated into French, and is in FNAC in a more mainstream kind of presentation than in the UK. Of course, most things are available online and second hand these days.
If you're near a Daunt's bookshop, they used to have literature organised by geography.
"Hammer and Tickle" (Ben Lewis) for jokes throughout the period
Viktor Pelevin (-perestroika and post-) is brilliant, but wait till you have a better idea of the background before tackling his stuff. (though if you are a Buddhist, that might be a way into his work)