Hi there Bill, thanks for your question. Congrats on your new job! This is my area of expertise and there are quite a few areas around Beverly Hills that will fall within your price range. Specfically, I am thinking Culver City, Beverlywood, Beverly Center/Miracle Mile, and possibly some parts of Hollywood Hills.
I specialize in not only sales but also do many rentals in this range so I could send you some prospective properties if you like, or give you more advice as to the best commute. Contact me anytime!