When is the best day to go, ie less crowded?
Best exhibits?

The exhibits/tours do not change day to day, and really the day of the week doesn't make much difference. Sundays are a little more crowded but the complex can absorb the crowds very well. After 4PM any day will be less crowded - but on some days that only gives you 2 hours which is not enough time.

Entrance is free and unlimited, but parking is VERY limited. You must make advance parking reservations for a specific time.

The parking restriction really help to manage and limit the crowds.

I would think attending on a week day would be the least crowded. Although, reservations are no longer necessary on weekends or per the website, any day in August either. http://www.getty.edu/visit/planning/reservations.html

Actually Barbara, I know it is counter-intuitive -- but weekdays are MORE crowded than most weekends. I haven't yet figured out why but the 4 times I've been there have borne that out.

I'd have to agree that I've found the Getty to actually be busier on the weekdays. One of the guides explained that there are far more tour buses during the week.