Glenbrook is a neighborhood of the city of Stamford, Connecticut. Spanning an area of about 1.7 square miles, about 15,400 people live in Glenbrook as of 2007. Glenbrook is located on the eastern side of the city, east of Downtown, north of the East Side and the Cove sections and south of the Springdale section. To the west is Downtown Stamford and to t…Glenbrook is a neighborhood of the city of Stamford, Connecticut. Spanning an area of about 1.7 square miles, about 15,400 people live in Glenbrook as of 2007. Glenbrook is located on the eastern side of the city, east of Downtown, north of the East Side and the Cove sections and south of the Springdale section. To the west is Downtown Stamford and to the northwest is Belltown. To the east is Darien.