Washington Square Park is one of the most famous chess historic venues for chess, ranking alongside the Cafe de la Regence. I’ve played there a few times but not during its glory days. In films such as Searching For Bobby Fischer it was portrayed as being frequented by famous players such as Israel Zilber and Kamran Shirazi. But they are not there now.
Here’s a video which give a taste of how it is these days. All in all you’re probably better off visiting one of the better chess servers: