That first parade was held in Union Square, New York City, and would be for decades to come.
But despite its name, Union Square has little else to do with unions -- originally named Union Place in 1815 after the intersection of Bloomingdale Road (aka Broadway) and the Bowery. Nonetheless, it's been a hotbed for protest for both labor movements and other activist organizations and remains so to this day.
Labor Day was officially recognized to ease labor unrest and prevent further violence.
In the years that followed the 1882 parade, Labor Days began cropping up around the country, in tandem with the general workers movement. Some states and municipalities recognized the Labor Days as public holidays with Oregon leading the charge in 1887. But it was incidents like the Haymarket affair and, a decade later, the Pullman strike of 1894 that galvanized politicians into action. After President Grover Clevelend sent federal troops to Chicago to crush the strike, dozens of people ultimately died. AH Raskin, the New York Times' chief labor correspondent once described the event as "what most experts now agree was the most flagrant act of strikebreaking by injunction in the nation's history." President Cleveland made Labor Day an official national holiday in the aftermath, but was still not re-elected that year.