The Gun Store, Battlefield Vegas, Range 702, and American Shooters are all fun local rental ranges catering primarily to the visitor market, I believe they all rent full auto weapons and a variety of other firearms as well. I've shot at all of them (Las Vegas resident) from time to time. Its a lot of fun, and the RO's are usually pretty experienced and stress safety- i've taken a variety of non-shooters including clients from Europe and Asia before and they've really enjoyed it. Call around for the best price and the experience you want.
If you have your sights set on any particular platform (MP5, Thompson, AK etc). i'd visit the websites of each, see what they have available and then call ahead to make sure they are up and running. These guns see a lot of rounds through them and occasionally are taken out of service for repairs. Have fun!