Yeah, you should definitely swap out Gillette with the Boston Garden (TD Garden) home of the Bruins and Celtics. Foxboro is over 30 miles from Boston. Harvard is certainly acceptable, though, since Harvard Business School and Harvard Stadium are right across the river from Cambridge in Boston.
You're missing the point! Most of it is in Boston, but the quiz refers to the whole metro area. (Which certainly includes Foxborough; it theoretically goes all the way up to Dover, NH.)
The description of the quiz states: "Name the subjects of pictures related to the CITY of Boston," NOT related to the Boston metropolitan area. Unlike the Red Sox, Bruins, and Celtics, the New England Patriots, who play at Foxboro, do not even have Boston in their name. Not missing the point, just disagreeing with the premise.