During the 1880's, the western tip of Long Island in New York was in many ways beyond the authority of the city government to control and therefore became a sanctuary for illicit activities of all sorts, such as prostitution, mugging, drunkenness, and the like. This was somewhat exacerbated by the relative proliferation of saloons, cheap hotels, and other houses of ill repute, especially in the area then known as West Brighton, which now forms the basis of the modern Coney Island. Beginning with the first railroad lines that connected the area to New York City proper in the late 1870's, other, more allowable sorts of entertainment (aside from the sedate summer homes New Yorkers had kept on Long Island for years) began to spring up. Family-type hotels were the largest of these, although the other types of entertainment that you wouldn't tell your mother about certainly remained popular in the area as well. The illicit growth in the area was stimulated under Tammany Hall politician John McKane, and it even earned the popular appellation, "Sodom by the Sea."
At about this time, in 1882 to be exact, a very original hotel was built in West Brighton. Known as the Elephant, it was a huge sculpture of its namesake made of wood and covered with tin. It had spiral staircases in its hind legs, a diorama and cigar store in its front ones, and an observatory in its head. The body of the thing was filled with guest rooms and had a shopping mall inside, as well. Although I have not been able to get any definite information as to size, based on the picture I am currently looking at it must have been about seventy or eighty feet tall if one counts the striped gondola on its back.
This elephant became a staple of the West Brighton area. If you went on an outing to the island, the elephant was all but mandatory. The thing made such a dent in consciousness in New York that it became reasonably common to say that you were going to "See the elephant" as a euphemism when you were in fact going to take advantage of the other, less safe and more scandalous attractions of the area. So if you ever meet someone from the 1880's, be aware that if they wink at you and ask if you want to go see the elephant, you're much more likely to wind up in a brothel than a zoo.
I have been unable to discover whether or not this has anything to do with the children's song Miss Mary Mack, who wanted to go see the elephant jump the fence. Without definite evidence placing its origin before or after this period (which is especially hard to obtain when the subject is folklore which is by definition elusive with regard to hard evidence), it is impossible to say for sure whether the two are related.