"You got a face with a view" is a line in that Talking Heads song.
It seems to me that "face" and "view" are mirror images in a word sense.
"Face" or
facie, is a replacement word in English. Like so many other names of body parts, face replaced the Olde English
ondwlita or
andwlita which survived briefly in Middle English as
anleth (there are other humorous Anglo-Saxon names for body parts at that first link).
Given the Norman Conquest, I first looked to French to see a deeper meaning of face, but the French gave up using face for "front of the head" in the 17th century and replaced it with visage (older
vis), back-formed from Latin
visus "sight" which derived from the Latin verb
videre. Of course our word view derives from
videre as well.
Now vision and view also mean sight and there is a parallel Germanic etymology behind the word sight. In modern German,
das Gesicht means face (in which you might see the root
Sicht, cognate with the English word sight = view). But there's an even older German word,
Antlitz (used only poetically these days much as we'd use visage).
Antlitz in turn relates back etymologically to the Old English
andwlita. It is like a face in the mirror.