"You got a face with a view" is a line in a Talking Heads song (see previous post). Another blogger was inspired by the same David Byrne phrase: link. I'm not so hooked on the E.M. Forster nuance (though I did enjoy the filmed version). "Face with a view" also pinged my brain 30 years ago when that song first came out.
It seems that "face" and "view" express a sort of grammatical/real world reflection.
Face or facie, is a replacement word in English. Like so many other names of body parts, face replaced the Old English ondwlita or andwlita (which survived briefly in Middle English as anleth). Given the Norman Conquest, we might look to French to see a deeper meaning of face, but the French gave up the use of face for "front of the head" in the 17th century and replaced it with visage (older vis), back-formed from Latin visus "sight" derived from the Latin verb videre. Of course 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. What a strange circle. It's like looking at a face in the mirror.