By LAUREN SCHUCKER BLUM

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.”

In the latest plot twist for downtown L.A., gritty is giving way to hip gentrification, with million-dollar condos, new restaurants such as Bestia and hot spots like the Ace Hotel. And although downtown L.A. includes Skid Row, a 50-block neighborhood with the highest concentration of homeless people in the country, an influx of affluent new residents like Mr. Sugarman and Ms. Hart signal the dawn of a new era downtown…

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