Here's a (subjective, of course) list of movies I'd recommend for both language acquisition and a better understanding of social background that might, to an extent, be helpful when you head over there. Asterisked are the titles that are more or less within the realms of mainstream movie industry, with the rest being a bit more of a highbrow arthousey fare.
Брат (Brother), 1997 * - a must see for a first-approximation understanding of what the nineties meant for an average Russian, and what Saint Petersburg looked and felt like after the dissolution of USSR
Брат/2 (Brother 2), 2000, a much more commercial sequel
Стиляги (Stilyagi, or "Hipsters") 2008 * - about non-conformist youth of the late 50s, a musical
Лето (Summer), 2018 - about non-conformist youth of the 80s.
Русалка (Mermaid), 2007 *
12 (2007) *
Аритмия (Arrhythmia) 2017 *
Дурак (The Fool), 2014
Левиафан (Leviathan)
Late nineties- early noughts movies critically readdressing the Soviet past:
Космос как предчувствие (Dreaming of space) 2005
Восток-Запад (East/West), 1999 *
For more info on individual titles, check out IMDB.
Most of these are highly critical of either the Soviet past, or the realia of modern Russia (Putin's Russia, as some might call it), so you shouldn't have much trouble finding them on mainstream online platforms (Netflix, amazon prime).
On a separate note, here's some mini-series for after-dinner binge-watching:
Эпидемия (To the lake, 2019) ** - for a glimpse into modern Russian series-making
Приключения Шерлока Холмса и доктора Ватсона (The adventures of Sherlock Holmes and Dr. Watson) 1979 - mid80s. A quality take on Mr. Conan Doyle's classic, very slow-paced, but very, very well done.
Let me know if you have any questions or suggested changes to the list.