Finding Lick Brook can be a bit tricky. From Cornell, go through Ithaca to Route 13 south. Just past Treman State Park, the highway divides. Bear left and follow Routes 96 and 34 south. Immediately after the overpass, turn left to reach the northbound lane of Routes 96 and 34. At the stop sign, turn left. Stay in the right lane and go about 0.1 mile, watching carefully for a dirt road on the right, which leads to the parking area and trail near Enfield Creek.
Follow the yellow signs and white blazes of the Finger Lakes Trail east along the forest edge toward the railroad bridge. Follow the Finger Lakes Trail across the small stream (note, you will get wet feet) along the base of the wooded slope. The pipeline (a cleared swath) marks the southern edge of Babcock Preserve. The northern edge is at Lick Brook.
Another approach is from the top of the hill, via Townline Road. This is a beautiful, but circuitous and more arduous, approach. From Cornell, go through Ithaca to Route 13 south. Just past Buttermilk Falls State Park, turn left on Sandbank Road. In 1.6 miles, the road forks. Bear right on Townline Road and park on the right side, just before the creek. The trail, also on the right, is clearly marked. It runs alongside Lick Brook, crossing the brook at the bottom of the hill where you enter the Babcock Preserve.