This is one of the rare instances where I can't describe a street as being "between" two avenues. Sure, the west side is bordered by East End Ave, and I suppose if you really want to get technical, its other side is clipped off by the FDR drive (but really it's the East River). Maybe it's just that "84th St Between East End Ave and a sheer cliff into the East River" doesn't have a good ring to it. Besides, this little nub of a street has its own moniker, so let's use it!

Gracie Square – named after the same Gracie family as Gracie Mansion, a few blocks to the north  – marks the southern-most edge of Carl Schurz Park and was not called as such until 1929 when Anothony Paterno built his bizarre "1 Gracie Square" building on the corner.

1 Gracie Square is perhaps best described by the 2007 New York Times article: It’s One Building, but It Looks Like Six

The Gracie Square side is an interlocking puzzle of vertical runs of quoining, horizontal courses of stone, irregular balconies and oddly placed moldings.
Even the brick varies: the east section is a darker shade than the west. The theme is carried down to the first-floor walls, where the limestone was carefully cut and laid in irregular blocks, as if they had been built with scavenged material.

The rest of the buildings on the block feel rather ordinary in light of the oddity that begins on the corner. But there's still some wonderful stuff to behold. The north side of the street is, as expected, the edge of the park with it's rusted fence and standpipes.

Towards the end of the street, there's a short pathway which brings you to a river-front promenade. Which is all well and good, but I much prefer what comes right before that: A scary, industrial pit which provides maintenance access to the FDR Drive below. Looking like something out of a Saw movie, the concrete hole in the ground is surrounded by low-rise fencing and wraps all the way around the eastern-most building. It's such a contrast to the surrounding buildings; whomever designed this must be an evil genius.

...And then there's the river with its beautiful views, blah blah blah (The dank pit is better).