Black Gulch Trail goes from Keyesville Rd up to Rancheria Rd, access it at a turn off across from the campground at the bottom of the dam. There are a couple of places to turn off of Keyesville Rd before you get to the trail, go left at the saddle to get to a nice lookout over the valley with a nice climb to the top. Going up Black Gultch Trail there are a couple of other routes off to the right, you can do some exploring up there. Right before you cross the creek the first time there is a trail up a hill to the right, which is Borderline Trail and it comes out at the back of Evans Flat campground, or drops off to Sawmill Rd and back to the valley. You can make a loop of it if you go up Borderline and back down Black Gulch. The top of Black Gulch is at Davis Camp, along Rancheria Rd.
Sherman Trail is to the left off of Sherman Pass Rd. Go up from Kernville maybe 15 miles, turn right onto Sherman Pass Rd, go 4-8 miles and look for Sherman Trail to the left. Near the top of the ridge you can turn off onto a dead end trail that goes to the top of Sherman Peak for a fabulous view.
There is also a trail that goes to Monache Meadow, which is a cherry stem into the Golden Trout Wilderness, where you can access the South Fork of the Kern River. Monache is a great place to camp for a weekend. Go up Sherman Pass Rd and go left at the fork towards Black Rock trailhead, then the route to Monache is to the right.
The Forest Service map of the area, Sequoia National Forest, will show all of these routes. All of the trails are easy, but they're fun and scenic.
Have fun,