There are lots of great places to hike in Pulaski Co. Your best bet is to go get a trail map at the U.S. Forest Service ranger station for the Daniel Boone National Forest. The station is on south monticello street, just before it runs into US 27 (near Bob Evans).
One of my favorites is the trail at Bee Rock recreation area, that ends at "the narrows" of the Rockcastle River. (Head east on 192 at toward Mount Victory, almost to the Laurel Co. line). In the same area, the Nathan McClure trail is a nice trail that follows the shore of the upper part of the lake, where it looks more like a river. Just don't go in high water, when the trail might be submerged. (Not a problem for the next 5 years.)
There's some good information here:
Somerset District Campgrounds
Also, down in the Cumberland Falls and Yahoo Falls area of McCreary Co. (not in the county, but closer than BSF) there are a ton of trails, including lots of access to the Sheltowee Trace).