The grassy center of Monument Sq is a favorite resting and picnicking spot for cyclists touring Concord's scenic roads. At the southeastern end of the square is Wright Tavern, one of the first places the British troops searched in their hunt for arms on April 19, 1775. It became their headquarters for the operation.

Old Hill Burying Ground, with graves dating from Colonial times, is on the hillside at the southeastern end of Monument Sq.