Davenport Center is located, as the name suggests, in the center of the town of Davenport, in the Charlotte Valley. Charlotte Creek flows along the northern edge of the community on its way west to the Susquehanna River at Oneonta. New York State Route 23 passes through Davenport Center, leading west 8 miles (13 km) to Oneonta and east 18 miles (29 km) to Stamford.
According to the United States Census Bureau, the Davenport Center CDP has a total area of 3.1 square miles (8.1 km2), of which 3.1 square miles (8.0 km2) is land and 0.04 square miles (0.1 km2), or 1.28%, is water.[3]