Like the OP, I was a huge fan of Simon and Garfunkel during my last years in school despite most of my peers probably thinking they were a brand of sauce or something.
'America' is also one of my all-time favourites although I used to find it quite eerie when I was younger for some reason. My other favourites are definitely 'Leaves that are Green,' 'Poem on the Underground Wall' and of course 'The Only Living Boy in New York."
One of the things that draws me to Simon and Garfunkel's music is how it captures the seasons and 'Leaves that are Green' is an obvious example of this. I find it quite an uplifting song, although it does deal with loss, and I particularly enjoy some of the interesting chord choices. 'Poem on the Underground Wall' is one heck of a wordy poem but it is sheer brilliance (particularly that the poem written with a crayon on the underground wall turns out to be a "single worded poem comprised of four letters") and most of the live recordings feature some pretty nifty guitar work from Paul.
As regards "The Only Living Boy in New York," it is without a doubt one of the more sad songs from the duo and it always does the trick for me when I'm in a certain mood. Very simple lyrics granted but the song has also become increasingly poignant to me in recent years. The background vocals/ echo chamber parts definitely help make the song for me. Quality!