Greenwich Village has a radical history that stretches back many decades prior to when when the folkies took up residence. At one time some artists decided to secede from the USA and declared Greenwich Village to be “The Free and Independent Republic of Washington Square” [0]. Apparently there's a staircase inside the arch in Washington Square and you can climb to the top but I've never seen it opened to the public as opposed to the Soldiers' and Sailors' arch in Grand Army Plaza (Brooklyn) which is occasionally open to the public (usually during the annual Open House New York).
[0] https://ny.curbed.com/2017/1/24/14372316/greenwich-village-w...