The two museums are relatively close (though a slightly longer walk than most Angelenos would care to take) and focus on recent works as well as the gems from the permanent collection. A single fee gets you into both (as well as the MOCA Pacific Design Center in West Los Angeles), and you can easily visit both in an afternoon. Plus, if you end your trek at the Geffen, you're in Little Tokyo and can decompress with a bowl of udon or sweet bean cake.