I always find these fascinating, perhaps because they are seldom remembered now, but also because I paid little attention then (that was girl stuff - you might get cooties from even paying too much attention to it), but such is my memory that even a few years later I remembered these things better than some girls who played them. Not on this song in particular, but even in highschool I would note at lunch table when they were reminiscing, some girls knew them cold, and others just looked blankly. And in college, going to school 700 miles away, scraps would emerge in discussion and I would be surprised that these girls from Virginia (or New York or North Carolina) had the lyrics wrong! It was a further education in folk music, and I eventually learned that even a few towns over there could be subtle changes.
The phrase "turn to the east, Sally, turn to the west; turn to the very one that you love best" came to me today out of nowhere and I had to work to reconstruct it. My wife, who grew up a hundred miles away knew a similar, perhaps identical version and I enjoyed working it out with her. It is "Little Sally Walker," which is Waters in some versions and maybe was in New Hampshire as well. My memory is not that exact. Girls stood in a circle with one in the center. She would stand, then crouch, then stand up again and begin spinning, stopping in front of another player at the end, who would becoming the next Sally.
Little Sally Walker
Sitting in a Saucer
Rise, Sally, rise
Wipe away your tears
Turn to the East, Sally
Turn to the West
Turn to the very one that you love best.
It occurs to me that I could have exploited this by entering the game and seeing who chose me (Whoa! Let's take a closer look at Joanne!) or not-so-subtly declaring who I liked best. But that was a level of social courage I did not possess, and by the time I did, girls didn't play games on the playground anymore.
There are not only other versions, but racier ones, including one by an Australian rapper a decade ago. It most likely comes from early 19th C England and then jumped to America. Except things didn't jump the ocean from GB as much 1776 -1920, so it may have been older than that, with separate versions developing. Reading the origin stories is an exercise in people just obviously making stuff up based on chance sound associations. When the just-so story only explains your version from Camden, and doesn't fit the one from Trenton or Philly, it ain't likely. Still fun to read, though.
It is supposedly very African-American, but its popularity in New Hampshire in 1960 suggests that is not a full explanation. My female readers hail from all over the East, so I would be interested in your versions.