The Seneca River flows 61.6 miles through the Finger Lakes region of Upstate New York in the United States. The main tributary of the Oswego River – the second-largest river flowing into Lake Ontario – the Seneca drains 3,468 square miles in parts of fourteen New York counties. The Seneca flows generally east, and is wide and deep with a gentle grad…The Seneca River flows 61.6 miles through the Finger Lakes region of Upstate New York in the United States. The main tributary of the Oswego River – the second-largest river flowing into Lake Ontario – the Seneca drains 3,468 square miles in parts of fourteen New York counties. The Seneca flows generally east, and is wide and deep with a gentle gradient. Much of the river has been channelized to form part of the Erie Canal.