This U.S. state's oldest school, Berwick Academy, overlooks the Salmon Falls River which forms part of the state border with New Hampshire. Name the state.
Berwick Academy (Maine):  Founded in 1791, it is the oldest educational institution in Maine and one of the oldest private schools in North America. Berwick Academy (Maine):  The school sits on a 72-acre, 11-building campus on a hill overlooking the Salmon Falls River, near the border between Maine and New Hampshire. Salmon Falls River:  It rises at Great East Lake, Newichawannock Canal, and Horn Pond and flows south-southeast for approximately 38 mi , forming the border between York County, Maine, and Strafford County, New Hampshire.
Maine