The oldest park in the country dates back to 1634 and several others almost as old. The link goes to the list from the Trust for Public Lands
America's Oldest City Parks
Many of the United States' oldest city parks are also its most revered. Boston Common, set aside in 1634, remains one of the most heavily used public spaces in the U.S. And Rittenhouse Square--one of four public squares remaining from those laid out by William Penn in 1682--is considered one of the finest examples of an urban park.