About 1,800 feet above the Pacific Ocean, atop a steep mountain overlooking Topanga Canyon, sits a compound with a storied past and some of the biggest views in the city.

From the property's 60 acres, nearly all of Los Angeles—a city known for its expanse and fragmentation—comes together in one frame. The Valley, downtown, the Westside, the South Bay, Catalina and the entire Santa Monica Bay are visible.

The...