Haymarket Square is the historic name of a former town square in Boston, located between the North End, Government Center, the Bulfinch Triangle, and the West End. The square was a well-known feature of Boston from the mid-19th century to the mid-20th century, when the buildings around it were demolished to make way for the Central Artery and Governmen…Haymarket Square is the historic name of a former town square in Boston, located between the North End, Government Center, the Bulfinch Triangle, and the West End. The square was a well-known feature of Boston from the mid-19th century to the mid-20th century, when the buildings around it were demolished to make way for the Central Artery and Government Center. The Haymarket produce market continues to operate at a location near the historic site of the square. The Haymarket MBTA station extends under the former site of the square.