Teresa,
once you find out if busking itself is legal in LV, you might check with some of the casinos (like the Excalibur/MGM/Circus) and find out if busking on their rounds is allowed. Some of them have large, park-like surroundings and if the type of music you play fits with their theme you might be able to find a nice place, off the street, with a constant audience (and maybe some shade!)
Cheers
PB