Just to be clear from the top, this medal does not commemorate the 200th Anniversary of New Rochelle, NY, it is medal commemorating the US Bicentennial that was issued by New Rochelle.Many cities/counties/States across the US issued commemorative medals to help celebrate the US Bicentennial in 1976 - New Rochelle, NY was one such city.
The obverse of the medal presents conjoined portraits of George Washington (forward) and Thomas Paine (rear); an American Eagle is depicted behind the portraits (top) with a horseback rider (Caesar Rodney?) within a constellation of 13 stars (below). The central portraits/devices are encircled by two rings of inscriptions: "1776 - New Rochelle - A Bicentennial City - 1976 " and "These Are The Times That Try Men's Souls" forming the outer ring, with "The Constitution is the Guide Which I Can Never Abandon" forming the inner ring. The "These Are the Times" quote is a quote that appeared in Thomas Paine's December 1776 pamphlet titled "The American Crisis". It referred to tge then-current difficulties that Washington and the Continental Army were experiencing.
The medal's reverse is a collage of elements. At the center is a standing figure of George Washington, he is encircled with smaller depictions of various waypoints of his career - from his time as a civilian Surveyor through his development as a military officer/leader (first with the British, then against them).
Washington was the Commander-in-Chief of the American Continental Army that successfully fought against the British in the American Revolution and was the first US President under the US Constitution. He is considered a Founding Father of the United States.
Paine, also a Founding Father, was an advocate for American freedom from British rule. He is well-remembered for his "Common Sense" pamphlet and other writings that supported the American independence cause; his writings used straightforward language and were directed toward the general public.
The medal was designed/sculpted by Michael Lantz and struck by the Medallic Art Company (MACO). It was sponsored by the New Rochelle (NY) Bicentennial Committee.
The 1-3/4" high-relief medal was available in gold-plated 0.999 fine silver (Mintage 250; Issue Price: $60), 0.999 fine silver (Mintage 500; Issue Price: $35) and Bronze (Mintage UNL - 1,000?; Issue Price: $7.50)
1976 New Rochelle (NY) Bicentennial Medal

For other of my posts about commemorative coins and medals, including the 1938 New Rochelle half dollar, see:
Commems Collection.