MOCA's (moca.org; free) notable art collection focuses mainly on works created from the 1940s to the present. There's no shortage of luminaries, among them Mark Rothko, Dan Flavin, Willem de Kooning, Joseph Cornell and David Hockney, in regular and special exhibits.
MOCA's Little Tokyo offshoot – Geffen Contemporary at MOCA – is a quick DASH bus ride away; catch it at the corner of Grand Ave and 1st St. If driving, parking is available at the Walt Disney Concert Hall ($9 with MOCA validation).