It's legal to own almost all guns in Nevada, from a .22 pistol to a 50-caliber M2 machine gun.
You can't fire an M2 indoors, of course. A quick burst would take out the whole back wall of the range -- this gun can literally destroy a lightly armored vehicle. In fact, you can fire an M2 only from a tripod or mount and in general, you have to hang for dear life onto the two handles behind the firing mechanism; the trigger is a large button in between the handles that you press with both thumbs. In Nevada you could, legally, take it out to the desert and really tear up the landscape, though you might attract some attention.
At the indoor ranges, you can fire any handgun (even the big ones like .44 magnums), as well as machine pistols, also known as submachine guns or SMGs. If you don't own them, you can rent them.
As for the SMGs, the Israeli UZI, for example, uses 9mm ammunition, which is small compared to .44s and .45s, so the damage is (in general) less per round, though the rate of fire is nothing short of spectacular. The Russian AK-47's rate of fire is listed at six hundred rounds a minute, which translates into ten rounds a second, so it takes a mere three seconds to empty a 30-round magazine, which is quite a thrill, though not very accurate. The recoil of each round raises the barrel, so if you're not trained in firing SMGs, the last 29 rounds wind up sailing over the top of the target; the last few rounds could go 20 feet over.
But we digress.
Several gun stores/ranges/clubs are scattered around Las Vegas and Henderson. Representative is the Gun Store at 2900 E. Tropicana Ave. Here, you can rent a dozen different submachine guns/pistols, such as M16s and AK47s (.223); UZIs, Stens, and MP40s (9mm); and M3A1 Grease Guns and Thompson M1A1s (.45). They rent for $25 to $50 (depending on the caliber), which includes 50 rounds of ammo. But be prepared to buy several hundred rounds for guns with 25- to 35-round magazines that, as we mentioned, you can empty in one burst (the best way to practice on full-auto is with highly controlled bursts of 2-3 rounds). You can print out a $5-off coupon from www.thegunstorelasvegas.com.
At the Gun Store, you can also rent a variety of handguns, buy ammo and targets, and generally blow off cordite till you run out of money.
The Las Vegas Gun Range and Firearms Center is similar. It's located at 4610 Blue Diamond Rd., 702/386-4867, and has indoor ranges for both handguns and rifles.
And if you're really serious about your shooting (in terms of speed and accuracy), you should look into Front Sight, a 500-acre "gun resort" about 40 miles west of Las Vegas on the way to Pahrump, the largest non-military firearms and self-defense training facility in the U.S. Check it out at www.frontsight.com.