Frances Anderton, host of the KCRW show DnA: Design and Architecture, asked me that very question. (RealPlayer link here.) For me, the answer was obvious: City Hall. Designed by the firm of Austin, Parkinson, and Martin and finished in 1928, the building was damaged in the Long Beach earthquake and re-opened just months after I took office in 2001. It contains sand from each of California's 58 counties and water from its 21 missions. There are some great detail photos at Project Restore's homepage, but none of them capture what it's like to come to work here and be able to look up at the magnificent design, knowing that this is the public's building. To those readers who've never seen it, you should take the red line downtown on a Tuesday, Wednesday or Friday and see Council Chambers when it's a living temple of democracy. Then take the elevators up to the 28th floor, and walk up the stairs into the Tom Bradley Room, from whose balconies you can see a whole lot of Los Angeles.
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