The Cayuga Trail is a long loop trail that runs on both sides of Fall Creek.  It starts just across Forest Home Road from the Cornell Arboretum, and goes upstream to cross the creek at Route 13 before heading back (see orange lines on bottom map below).  The trail runs through forests, agricultural fields, and along steep cliffs.

Links to Monkey Run and Cayuga Trail:
http://ludlow.dns2go.com/cribbage/areas/cayugatrail/CayugaTrail.html
http://www.plantations.cornell.edu/collections/natareas/Public/Monkey/Monkey.htm
 

The Overhangs:
This area is not on the official Cayuga Trail (perhaps for safety reasons?), but offers the unique prospect of standing next to a hemlock tree with nothing but several inches of dirt between your feet and empty space below.  The rock and soil below have eroded away, while the tree roots hold large sections of ground suspended above perhaps a 50 foot drop.  Every year a few more trees tumble down the abrupt slope into the creek.  Given these conditions, I must advise great caution if you visit The Overhangs, to avoid causing erosion to the slope or mortal injury to yourself.  The location of this area is represented by the red star on the maps below.  There are two ways to reach it.  The shortest approach is reached by driving into the Cornell agriculture fields (blue line below) that are just past Varna on Route 366.  From near the back corner of these fields, find your way back to the creek and follow it upstream.  There's a steep, sometimes muddy climb to reach higher ground, then you soon arrive at The Overhangs.  Alternatively, you can park at the end of Monkey Run Road just off Route 366 (contrary to these maps, Monkey Run Road is mostly closed to traffic and does not bridge Fall Creek).  From the parking area, continue north along the abandoned road (rather than taking the marked trail west).  This trail will pass the remnants of the Monkey Run Road Bridge and continue downstream.  Eventually it will turn west to follow the creek.  Some time later, this trail will bring you to The Overhangs.

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

Edited, map from http://ludlow.dns2go.com/cribbage/areas/cayugatrail/CayugaTrail.html