So why is prostitution legal on that bunny ranch, but nowhere else in the U.S.?
Nevada allows it completely, and as long as it's a regulated Brothel, it's allowed.
However, just because the state allows it, doesn't mean that the city allows it. I believe there may be a part of the law that says if the town / city / county has a population larger than X, prostitution is illegal. If it's smaller than, then it's A-OK. (Still in a Brothel only)
Technically, Las Vegas as a city has ordinances against prostitution, they just don't enforce them very strictly.