Then host the site in a country where prostitution is legal.

According to the article:

Early this year, the attorney general of Connecticut, Richard Blumenthal, representing 40 states, sent a letter to Craigslist demanding that it purge the site of such material and better enforce its own rules against illegal activity, including prostitution.

Craig's List voluntarily decided to curb the ads. Although they received a letter, it doesn't mean that they violated the law or were committing illegal acts themselves.

US newspapers have had these types of escort ads for a long time so I'm not sure why it would be illegal to do online.

Interesting idea, but if you made a site like that with the intent of covering the US and only the US, there would be problems: it's not legal if you're hosting it in another country only to bypass restrictions. (ThePirateBay, for instance, is legal because it serves as a hub for countries where torrenting isn't as illegal. If it were an only-US service, then it would be in trouble.)

Are there any sites for other parts of the world that already deal in this? Perhaps they would have the biggest opportunity for crossover here.

Quite the contrary; black market companies usually are very profitable (if you're able to deal with the risk).

Yeah it didn't work for Napster or YouTube ... oh wait

It didn't work for Napster. The Napster now isn't the same as the one from the 90s. The Napster now legally sells music. Just like iTunes, Amazon, and Wal-Mart online.

And Youtube is still being sued for not removing copyrighted videoes. And they've yet to prove to actually make any money off of it.

Well it's been over 10 years and you're still talking about Napster. I'd say it worked.

You could incorporate in Nevada...