Goat Mountain is a seldom-visited peak overlooking the North Fork of the Boise River. Its lonesome summit is very worthwhile; the reason it is climbed so seldom is that it is very hard to get to. But if you make the effort, you'll find it a wonderful area, with multiple lakes, wildflowers in August, and a great adjacent ridgewalk. There are also several other peaks in the area for the avid peakbagger: Shepard Peak, Silver Peak, and more.
Drive Highway 21 from Boise past Idaho City and over Mores Creek summit.
Turn off at the Edna Creek onto the Crooked River road, FS 384. This is a decent dirt road.
After about 4 miles, turn onto FS 312, which follows the Pikes Fork drainage to Jackson Peak. The road is now a little narrower and a little rougher.
When you get to the turn off for Jackson Peak, instead go straight. Note the sign warning of rough road ahead (no trailers). The road from here through Trapper Flat is quite rough, even BAD in places. If the road is wet or there is snow, a 4WD might be required. If it's dry and you're a good driver, you can get in with high clearance. I've done it in a F150 2WD pickup, and also a Subaru Forester. From the turnoff, it's about 6 miles through Trapper Flats and onto a saddle directly east of Wolf Mountain.
From the saddle, go about 2.5 more miles, some on a steep descent, but overall on a better road than Trapper Flats, to another saddle. (If you continue, the road from here immediately drops down to the North Fork of the Boise). Park here on the left.
Note that on remote roads like these, you should carry a backcountry driving kit including at least a shovel, saw, and possibly a second spare tire.
This area is extremely remote. From the time you leave the pavement, you will have left civilization and no one will know where you you are. Take precautions.
There are lots of primitive campsites in Trapper Flats. There are developed Forest Service campsites at the Edna Creek campground. Or you can backpack into the lakes under the peak (highly recommended!).
For additional information on this climb and other peaks in the area, please see Tom Lopez's excellent book, Idaho: A Climbing Guide
From the car, proceed across the road (south) and look for a game trail that initially goes up but then drops down just a bit. If it's not obvious, don't worry because it only goes a short ways.
Either way, just start traversing. Stay near the 8050/8100' contour and head for the saddle (obvious on the map, but you can't see it when you are hiking).
When you get to the saddle, continue slightly to your right to maintain the same general elevation until you get to the main drainage from Goat Lake. Follow the creek up past some beautiful little lakes/ponds, then on up to Goat Lake.
Go around the lake on the left and head for the obvious saddle to the left of what the map shows as the summit (it's not). When you reach this saddle, You'll see another small lake to the south. Above the lake, look for goat trails that go to the left of the fake summit, and access the summit ridge. When you get to the gendarme, pass it on the right by clambering through the rocks (easy Class 3).
On the return, try following the ridgeline that parallels your route into the valley. It's very scenic with lakes on both sides. If you go far enough, you can also count the summit of North Goat Mountain before dropping down to your car.