Rio Bravo is a classic Howard Hawks film. It's a fun Western that doesn't mind making fun of John Wayne. It was written by Leigh Brackett, whose last script was the first draft of "Empire Strikes Back." Even after rewrites, Leia is still very much a Howard Hawk woman.
If you like Carroll Baker, check out "Baby Doll" by Kazan. A really wild film with tremendous performances. It was also the inspiration for the "kinderwhore" look.
After all the "Mank" mania, I'm going to say it : "Citizen Kane." Even as a teenager who hated black and white movies, I found the movie to be surprisingly modern with its overlapping dialog, editing and cinematography.
If you want movies with more modern narratives, check out Pre-Code movies. The Hays code severely restricted the kind of content Hollywood could make (kind of like now). Some people argue that it neutered cinema (kind of like now). Check out "Baby Face" as a prominent example of Pre-Code film. I quite like "Employees Entrance" - the story still feels relevant.