To reach Yellow Barn, take Route 13 east from Ithaca, and turn right on Yellow Barn Rd before you reach Dryden.  Abandoned roads, snowmobile trails, and power lines offer several possibilites for a nice walk in the woods here.  On the map below, gray indicates paved roads (Tehan Rd turns into Signal Tower Rd as it turns south; Card Rd ends with a trail leading beyond).  Lavendar indicates gravel road passable by car, yellow indicates hiking (snowmobile) trails, and the dotted red line marks the passage of power lines (with at least a faint trail underneath).  Several trails lead east from Yellow Barn Rd, climbing up to the ridgeline to meet either Signal Tower Rd or to abandoned sections of this road.  At the very north end, the old road devolves into a series of dusty logging roads.  At the far south end, it does appear to be accessible from Irish Settlement Rd (if you look for it carefully).  From farther north on Irish Settlement, it seems possible to access the eastern section of Yellow Barn State Forest by way of the power line right of way, but I haven't put this to the test.

Edited, map from http://www.topozone.com