Los Angeles
The problem is, LA is huge, and cross-city traffic is among the worst in the country. There's virtually no spot that'll make you accessible for both Westside/SouthBay/LAX folks and Valley-area folks unless they're willing to spend upwards of an hour on the drive. So I second the idea of finding out where your clients are and staying there (or making a couple different stops, depending on length of trip).
But if you're counting votes, count me for the LAX/Culver City/Marina Del Rey area 
I had this discussion with a friend of mine who was making her first tour to LA.
I seems to me that you have 3 basic areas to set up camp. You have the West Side....LAX, Santa Monica etc.....Then you have the Valley....Woodland Hills, Studio City, Burbank etc....and third is Hollywood/Downtown-ish.
As a person who lives in the Valley it is a challenge (polite way of saying pain in the ass) to see someone at LAX because of traffic....I always appreciate it when someone stays up here. Of course if you are a West Side Hobbyist driving to the Valley sucks.......Patricia makes a good point the you should go where the majority of your clients are....or where they are willing to drive to.
If you make it up over the Pass let me know. 
The problem is, LA is huge, and cross-city traffic is among the worst in the country. There's virtually no spot that'll make you accessible for both Westside/SouthBay/LAX folks and Valley-area folks unless they're willing to spend upwards of an hour on the drive. So I second the idea of finding out where your clients are and staying there (or making a couple different stops, depending on length of trip).
But if you're counting votes, count me for the LAX/Culver City/Marina Del Rey area