We didn't catch the episode of History Channel's "Pawn Stars" to which you're referring, but we gather that earlier this year the team filmed an episode in which they took a bunch of pawned Civil War-era guns out to a range to fire them. This is usually inadvisable and the show's gun expert Sean Rich, who's the weapons advisor for Pirates of the Caribbean, explained the risk of an old gun exploding in the shooter's face.
The segment was actually filmed out in Pahrump at the Lone Wolf Range, which is a members-only gun range and a member of the Nevada Cowboys Action club. If you're looking for a shooting range in Las Vegas that's open to the public, we have several, however, including the Las Vegas Gun Range and Fiream Center (4610 Blue Diamond Rd.), American Shooters (1212 N. Boulder Hwy. and 3440 Arville St.), where you can shoot everything from handguns and rifles to machine guns and "exotics," and the Clark County Shooting Range, which has separate Shotgun, Rifle-Pistol, and Archery Centers (11357 N. Decatur Blvd.)
Coming early 2012, too, is the new Machine Gun Vegas gun range, which is billing itself as some kind of sexy ultra-lounge (sans alcohol), featuring sexy hostesses, in addition to a range of modern machine guns and assault rifles and famous firearms from World War II. (See Today's News 11/9/11, where you can also find details of how to apply for a job at this new facility.)