Ball Square is a neighborhood primarily in Somerville, Massachusetts, United States, but also extending into Medford, at the intersection of Boston Avenue and Broadway, located between Powder House Square and Magoun Square. It is primarily a residential area with a handful of shops and restaurants along Broadway. Located on the edge of the n…Ball Square is a neighborhood primarily in Somerville, Massachusetts, United States, but also extending into Medford, at the intersection of Boston Avenue and Broadway, located between Powder House Square and Magoun Square. It is primarily a residential area with a handful of shops and restaurants along Broadway. Located on the edge of the neighborhood surrounding Tufts University, Ball Square contains a mix of businesses serving the student and academic populations as well as those reflecting the more blue-collar neighborhoods to the east.