This is probably the cheapest place to stay in Greenwich. Its location is actually in Riverside, which is across the Mianus River. It's off a busy street, the Post Road, but the location isn't bad. It's not far from Greenwich, close to Old Greenwich and the beach, and not far from Stamford (a small city with lots of restaurants, theatres, and shopping).
http://www.hojo.com/HowardJohnson/control/Booking/property_info?propertyId=00749&brandInfo=HJ