LA
is a great area to stay in. Close to LAX and centrally located.
Hotels:
Shutters, Oceana, Lowe's, Shan-gri-la
To Do:
3rd street promenade(shopping and lots of food)
the beach
Malibu is a short and cool drive up the coast
Hollywood is a short drive away
Museum Row
Getty Center -architecture and museum
If you like classical music, go to The Disney Concert Hall. The acoustics are amazing. I f you are coming after june, the newly renovated Hollywood Bowl will be opened and it's gonna be great.
Dodger's game
If you want to stay in Beverly Hills, try the Avalon-very cool hotel right off Rodeo' drive.
As mentioned above, LA is spread out and wherever you are there is something interesting to do.
PM me if you want some more info.
Good Luck!