Park Slope - Quiet and Casual?
You might consider Soigne, a restaurant/ wine bar on Sixth Avenue around 12th Street, not too far from the 7th Avenue stop on the F train.
I know that "wine bar" implies small and tight, but Soigne has a full bar with comfortable bar seats, and a nice, attractive space with plenty of tables. It's conducive to quiet conversation.
The food ranges from good to excellent, and the price is right (or at least it was the night my friends and I dined there). They don't rush you at all, and I think you'd be welcome to linger over wine as long as you'd like.