For drama I would offer The Elder Son and Nameless Star.

For Action, the choice is a bit smaller, as violence wasn't as endorsed by USSR as it is in capitalist countries. There's a dilogy I know, heard good things about, but never got to watching properly myself: Zone of attention and its sequel. It's about marines and airborne forces have a joint exercise. Features soviet troop carrying hovercraft, among other things.

Idk if you would consider children's adventure movies to be action, there's Guest from the future, Adventures of Elektronik and Three Musketeers.

I also cannot recommend enough the soviet Sherlock Holmes TV series. It's charming, it's stylish and the final story (XXth century begins) hits some very heartfelt notes at the end. Relevant now perhaps more than ever.

That's for starters. Do you like spy stuff? Detective stuff?

Tarkovsky movies. I'd say Stalker at the top though the others are quite good as well.

Man with a Movie Camera is an early documentary showing some cities in the Soviet Union, it's silent but really well scored and entrancing I think.

Come and See is a haunting war film that goes through the trials and tribulations of a young man and his village as the Nazis act out barbarities.

The Cranes are Flying is a celebrated Soviet drama/romance/war film.

Battleship Potemkin and Strike! are Sergei Eisenstein films, silent about respectively the mutiny on the Potempkin which was a pivotal moment in Russia's revolutionary history while Strike! is a dramatic telling of a worker's strike and the resultant actions by the bourgeoisie, military, petite bourgeoisie, etc. Both striking innovative uses of cinematic techniques now common-place and taken for granted such as Eisenstein's montage technique.

The Ascent is another great Soviet war film, about two partisans that leave their group and though they face many foes they end up taking a journey into their very souls.

Snow Queen (1957) is an alright adaptation of Hans Christian Anderson's story. But the animation must be pretty good. It's reported none other than Hayao Miyazaki, the head and creative mind of Studio Ghibli fame said he was depressed early in his career and considering giving up animation given the state of things with Disney when he saw this film at a union meeting and it gave him new hope and new drive.

If you'd like Sci-Fi then "Planet of Storms"/Planeta Bur from 1962 might be interesting. Super high production it isn't, it never-the-less shows an interesting Soviet slant on things. Along those lines "Nebo Zovyot" is another sci-fi soviet film that's interesting.

Koo!