There are a lot of good museums in LA, but the Getty is my favorite. It's big enough so that you don't feel cramped, and you get to go outside between exhibits. The architecture itself is amazing, and the gardens are a great place to have lunch...since it'll take an entire day to explore this complex.
However, The Getty may have some ulterior motives, because at times there have been photography exhibits with incredibly bias and unfair captions right on the museum tags that sit next to the photos. Luckily, they have enough rooms that shows like this are easily skipped.
