Plenty of ghost towns can be found within a few hours' drive of Las Vegas.
Two caveats. First, in the true ghost towns, visitors, especially those rooting around the ruins and outskirts, need to be especially cautious of open mine entrances and ventilation shafts. Second, the protocols and etiquette of exploring true ghosts and semi-ghosts vary according to each area. We've been to a number of ghost towns all over the west, of which few of the larger and more accessible ones are true ghosts. In other words, most have residents, or at least a caretaker, who are naturally territorial about their little piece of the desert or mountainside; also, miners still work some of the claims, which are private property. So be sure to inquire locally about any restrictions that might exist.
The closest ghost to Las Vegas, Potosi, is also Nevada's first ghost town. It was settled in 1856 by Latter-day Saint pioneers from Salt Lake City, who managed to mine a few tons of lead before abandoning the place a year later. In 1861, miners from California reopened the lead operation; zinc was also mined here. At its peak, the mine, a smelter, and rock cabins that could accommodate 100 existed. Nothing much remains. To get there, take I-15 south to the Blue Diamond Exit (at Silverton); go west on NV 160. In about 20 miles is the little settlement of Mountain Springs; Potosi is on the left high above the town. You can see a large pile of tailings near the top of a cliff, which pinpoint the mine.
Another mostly ghost town, on the other side of Las Vegas, is Nelson. Take the freeway through Henderson and over Railroad Pass as if you're going to Boulder City, but turn south on US 95. Go 10 miles and turn east onto NV 165, a narrow paved road through Eldorado Canyon that leads 12 miles to Nelson. Way back in 1775, Spaniards discovered gold in these mountains, which is why they're called Eldorado to this day. A hundred years later, prospectors rediscovered the area and mined it through the 1940s. A few original buildings still stand.
Roughly 25 miles south of the turnoff to Nelson on US 95 is the town of Searchlight. It's not a ghost at all, but it is the location of mines that date back to the late 1890s; Searchlight began to boom in 1902 and reached its peak in 1907. (You can continue down NV 164 all the way to Cottonwood Cove on the Colorado River, a great little resort town that very few people who go to Las Vegas ever visit or even know about.)
The semi-ghost town Chloride is across Hoover Dam in Arizona (take US 93 60 miles south of the dam, then follow the signs into the hills). Chloride's boom began in the 1860s when silver was found on what quickly become known as Silver Hill; by 1920, the town had grown to 2,000 residents. But during World War II, when the cost of materials and labor shot up, the mines were shut down. The town, however, never completely died, and there's plenty to do and see there today, both of a touristy and adventuring nature.
The remains of Rhyolite are the best preserved of any true ghost in southern Nevada. It's a bit of a haul from Las Vegas: about 120 miles northwest up US 95 (toward Reno), four miles from the (relatively) big town of Beatty. Gold was discovered here in 1904 and at its peak, Rhylolite was a metropolis of more than 10,000, with several dozen saloons, a dozen hotels, and a dozen grocery stores. The boom was shortlived, however; by 1915, Rhyolite was mostly abandoned. Still, it was built to last, and today you can see a three-story stone-frame bank and a two-story concrete school, as well as the train depot, jail walls, and the Bottle House, which was built in 1905 with 50,000 glass bottles. Rhyolite is probably the most scenic and historic place to go metal detecting near Las Vegas, though it's no doubt been picked over for decades.