Wiseblood (1979) is based on a 1952 novel so it has both ends of the hotdog. It's a bit odd ball but very underrated. The performances are all amazing and it has a very Lynchian feel to it.
Carnival of Souls (1962) feels more like a 50s film and has a unique dreamy atmosphere.
The Day The World Caught Fire (1961) is a times very evocative and rarely gets commented on because it's a British entry into a largely American genre.
Do people talk much about On The Beach (1959)? The cold war never felt more chilling. Everyone has heard of Dr Strangelove (1964) but the comedy free version of the same scenario from the same year, Fail-Safe is as effective in my book.