After selling their sprawling mansion for about $37 million in the summer, businessman and TV producer Burt Sugarman and his wife, former "Entertainment Tonight" host Mary Hart, gave up lush Beverly Hills and moved to an area better known for urban blight: downtown Los Angeles.

"Our friends thought we were crazy to move downtown, but we love it," says Mr. Sugarman. "There's so much energy here. We can walk everywhere. There are people on the street—and not just homeless people."

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