Several gun stores/ranges/clubs are scattered around Las Vegas and Henderson. Representative is the Gun Store at 2900 E. Tropicana. 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 you'll empty with one four-second burst (though the best way to practice on full-auto is 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.
Two other stores that rent similar weapons at similar prices are American Shooter's Supply at 3440 S. Arville and Master Shooter Supply at 4017 W. Sahara.