You wont be climbing the "real" Stonewall Mountain, as it lies within the boundaries of the Nellis Range.
Stonewall Mountain is an extremely difficult hike, you must be in great physical condition, be acquainted with USGS Topographical maps and start hiking no later than 0900 hours.
The hike is a full 7 hours round trip (5 up, 2 down), and rated as one of the toughest we've ever done. This is also a summer hike, the 8000 foot peak will have snow in late fall through early spring.
USGS, 30x60 minute Goldfield and 7.5 minute Stonewall Spring are a must, you cannot do this hike without topos of the region.
Lida Junction (closest landmark to Stonewall) is about 180 road miles northwest of Las Vegas on US-95. The only thing there is the Cottontail Ranch, one of Nevada's fine brothels ("Always Open"). [37deg30.147', 117deg11.030']
About 0.3 mi north of the Junction on US-94, turn east on a dirt road (Milepoint ES 4.5) Reset odometer here.
Miles from Paved Highway...
As you hike up the dry wash you'll see that 4-wheel ATVs have been in the area, following the trails they've blazed provides a smooth hike. The ATV trail will leave the wash bed and continue over ground and then return to the wash, shortly after this point you'll look off to the Southwest and see a large rock outcropping on the ridge, just left of this outcropping is the target of your first climb.
Climb up to the Right of the scree/talus slope but staying Left of the outcropping. You'll reach a small clearing at the summit, from this point head South along the ridge. When you near the end of the ridge, bear to the left to circumnavigate the 30-40 foot cliff that ends this particular ridge.
At the base of the cliff continue up the knoll directly South. Once you've crested this, off to the Southwest you'll see the summit of the peak that is your ultimate goal. Continue South into the saddle [37d30.000', 117d02.866'] and climb the small hill in front of you. Once you've crested this, continue along the ridge to the saddle that separates it from the larger peak. Hike up the ridge from the saddle to the summit [37d30.833', 117d02.716'] and you have arrived.
The peak directly south of your position (equipped with a solar powered microwave relay station) lies within the Nellis boundary, and wouldn't offer a much better view than the one you currently have.
On a clear day you can see Mt. Charleston 150 miles to the Southeast, the idle assembly towers on the NTS, and of course, the installation on Pahute Mesa below you -- namely the TPECR site (Tolicha Peak Electronic Combat Range). This was a new facility for us, when we found it in 1995. It has a paved road into it (most roads at Nellis are dirt), and people were working there on the Saturday we climbed the peak. It's not as fancy or secret as Groom Lake, but it's still a worthwhile trek.
We also found many abandoned mine shafts, a Native American campsite, a log cabin and plenty of Big-horn Sheep -- plus a dead Mountain Lion, so be careful!