I already knew about the Broad museum, which opened to much fanfare in downtown Los Angeles in 2015. But it was only as I researched my recent trip to the city that I realized it had become one of America’s most important centers of contemporary art. I discovered three other notable museums in the city dedicated to cutting-edge works: a major new institution with a collection comparable in scope and quality to that of the Broad, and two smaller museums displaying up-to-the-minute pieces by lesser-known artists deserving of more attention.