Well, it really comes down to if you're planning on providing out of your residence. If that's the case, you'll need to find somewhere that's accessible, but private. Near some major freeways since everyone drives in LA. 405/101 area is good, (Sherman Oaks, Encino) Studio City near Universal is good, 10/405 is also good (West LA, Santa Monica, Westwood). Any of these areas great and centrally located enough to keep you available.
If you like a lot of night life open air activities, West LA/Santa Monica/Venice. If you like a more crazy urban, West Hollywood, Mid Wilshire. The Valley is a bit more laid back, and cheaper to Rent/Buy, but some people won't travel there (stuck up transplants to my city!) I'm an LA Native, so it's all good to me.
Unfortunately, LA is so damn big, you won't be able to be central enough to everyone who might like to come visit. So you may also want to set up incalls in other locations. I know several girls who don't live in LA at all, but will spend a few days every week at different hotels around the county offering that as their luxury incall.
Good luck, and Welcome to LA!
Dk