It's hard to answer a question about "luxury", when that word means such different things to different people, as evidenced by the answers here. The important thing is, what says luxury to YOU?
When I think of luxury, I think of an expanse of land, a large flat yard, beautiful landscaping, nice fit and finish to the property, pool, well kept up neighborhood, etc. The Platinum Triangle ( http://www.thebremnergroup.com/communities/platinum-triangle/
) is the part of Los Angeles with the most intrinsic value, and therefore, luxury, in the eyes of most people. It includes Bel Air, Beverly Hills, and Holmby Hills, and they call it Platinum for a reason: it's beautiful, precious, rare, and expensive! Large lots, lush landscaping, celebrities and captains of industry, mansions, (even the guest houses are more luxurious than most homes!)
Moving out from there, Brentwood, especially Brentwood Park, ( http://www.thebremnergroup.com/communities/brentwood/
) is luxurious, but in less posh sort of way. Brentwood has a small "community" feel. The views will run from downtown LA to Getty views to Century City to Jetliner and ocean views, or no view at all in the flats.
Hancock Park has a wonderful conservative, "old money" feel with golf course views; Little Holmby in Westwood feels grand yet somehow accessible at the same time. Cheviot Hills is like a miniature of Little Holmby.
Ultimately, luxury will be determined by your taste and your wallet, but rest assured, there are some very beautiful, luxurious homes in LA. Keep up with the Joneses!
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Certified Home Retention Specialist
Blogging at: http://TheBremnerGroup.com/blog