Hi Shannon You did not give very many details as to where your Grandmother lived? or a Surname. Although not far from Onondaga County I believe that this could very well be the Stony Island that is located in the Town of Hounsfield Jefferson County New York near Point Peninsula NY (The Road leading to Pt Peninsula is midway between Chaumont and Cape Vincent off Rt 12E). This Stony Point is on Lake Ontario. The Island is known for its wildlife and migratory birds and many local people fish the shoals around it for Small Mouth Bass, Walleye, Perch and Brown Bullheads (plus other fish). It is a Nature lovers paradise and well known in the area. I hope this helps you. Pat R