Although it seems to receive few visitors, this forest can offer pleasant and challenging hikes.  It can be reached from NY Route 13 by turning east on Bull Hill Road, or by taking any of a few roads south from the village of Newfield.  There are several trailheads from Chaffee Creek Road (purple arrows on the map below), most notably the pipeline access track, which forms an obvious intersection with the road.  You can either follow it north/uphill for a short ways, until you get to the state forest boundary near the ridgetop (beyond this point, fallen trees make the going difficult), or you can follow it south/downhill to the pretty creek that gives the road its name.  Both of these sections are steep but quite manageable.  From the place where the pipeline crosses under the creek, there are small falls both upstream and downstream (pictures below).  A trail follows the creek downstream for a short distance to a campsite.  It's also possible (though challenging!) to walk further south/uphill, climbing more than 500 feet in less than half a mile to a high ridgeline.  From here there are some nice views and an intersection of trails, one continuing to follow the pipeline south, another going a short distance to the west, another continuing a longer distance to the east, which I followed for about half a mile before turning back.  I suspect that this trail, an easily passable logging track, connects to the turnoff at Irish Hill Road (southeast corner of map below), where this road makes a sharp turn.  Those wanting an easier hike along the ridgeline could give this a try.

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