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?