Generally speaking, your best bet is to be doing this on a Friday or Saturday night, as those are the nights with the most people. More people = more clients, naturally. You'll see some action other nights, just not as much.
As for WHERE... really, it could be ANY casino I've listed below. There's just really no way to know. I suggest the one you are staying at because a) she might not go off with you if you meet her at Mandalay Bay and you are staying at Sahara (for reasons that should be obvious when you think about it) and b) she's probably not going to have a room, so it's going to be at YOUR room... thus you should check out the action at your casino bars first.
If I was doing this and wanted to stay at a casino where I would maximize my chances of winning this game, I would probably go with casinos on the Strip that are 4 star or better that have nightclubs on the premises. These will be places where a young lady in attractive, sexy clothing sitting at a casino bar won't stick out like a sore thumb: that's (going N->S) Wynn, TI, Mirage, Palazzo, Venetian, Caesars, Bellagio, Planet Hollywood, Monte Carlo, NY/NY, MGM, Luxor (kind of pushing the definition of 4 star, but they do have LAX) and Mandalay Bay. If you are staying at either of these properties and you are offstrip, Palms or the Hard Rock probably have some approachable ladies there as well.
That being said, I HAVE been approached ("Hey, are you looking for company?") at places like the Flamingo that aren't as trendy... so really, it could happen anywhere.
Like I said, this is quite possibly going to be less bang for your buck than a well-reviewed independent (since you WILL get to see them first, but you'll have no idea of the service offered until you get to the room), and the possibility for being ripped off and/or getting stung does exist, so keep your head on a swivel and think with the big head... but good luck to you.
-- Modified on 4/20/2008 8:20:15 PM