Good film, but it begs the question of how many Japanese dramas people have seen. It sticks to conventions pretty neatly and apart from weaving in a play (which wasn't very subtle), it's a very solid but textbook example of what Japanese dramas deliver and how they go about delivering it.
Kafuku is happily married to his wife. They have a good marriage, and they love to rehearse lines while driving. When Kafuku's trip is suddenly canceled, he returns home to find his wife in bed with another man. He leaves without them noticing. Before he can confront her though, she dies from a brain hemorrhage.
The lengthy conversations in pleasing settings, the slow pacing, the dramatic punch in the gut at the end, they're all staples of the genre. Hamaguchi handles them well, it's only the play that feels a bit too on nose and takes up too much time. Drive My Car is a perfectly fine film, but not worth the hype.