This path is accessible from Snyder Hill Road near its western end.  Not far beyond the house/office on the corner with Pine Tree, on the southern side of Snyder Hill Road, just look for the small triangular lot, follow the ditch back to the more defined footpath.  I don't actually know if this trail is public or private, but it seems fairly well maintained.  You soon pass a pen with sheep and chickens, then a small clearing with a large oak tree.  After hopping a tiny stream, you come out into a meadow favored by birds and deer.  The trail branches in places, and I haven't followed the various spurs, but if you continue in your original south-southeasterly direction, you should eventually hit a small park area.  To reach the park, you have to cross a small ravine, which requires a little scramble, but it's somewhat easier if you go down a bit to where the deer do their crossing.  From this park, you can follow the roads of the Eastern Heights subdivision back to Snyder Hill Road to complete your walk.

Map template from Tompkins County GIS