The Dead only played this once, in New York (surprise!) on 28 March 1972. It was the opening part of the encore, leading into One More Saturday Night. It was just a short instrumental, with no lyrics sung.
The song was originally written in the 1890's, and was used as a Presidential campaign theme in the 1920's.
The first is from the Digital Traditions lyrics database.
Down in front of Casey's old brown wooden stoop
On a summer's evening we formed a merry group
Boys and girls together we would sing and waltz
While Tony played the organ on the sidewalks of New York
East Side, West Side, all around the town
The tots sang "ring-a-rosie," "London Bridge is falling down"
Boys and girls together, me and Mamie O'Rourke
Tripped the light fantastic on the sidewalks of New York
That's where Johnny Casey, little Jimmy Crowe
Jakey Krause, the baker, who always had the dough
Pretty Nellie Shannon with a dude as light as cork
She first picked up the waltz step on the sidewalks of New York
Things have changed since those times, some are up in "G"
Others they are wand'rers but they all feel just like me
They'd part with all they've got, could they once more walk
With their best girl and have a twirl on the sidewalks of New York