visiting LACMA page for details.
Each Friday and Saturday evening through the summer, there are free concerts--Jazz on Fridays, Latin on Saturdays--at 6 PM in the main entrance court. We pack a picnic dinner and listen from above, on the balcony area of the Ahmanson building. Other families bring blankets and sit on the grassy areas around the plaza. If you get there really early, you can find seats right in front of the stage.
LACMA is free for all LA County residents between 3 PM and closing M-F. On Fridays, all of the galleries are open to 8 PM and BCAM and Resnick Pavilion remain open until 11 PM.
The LACMA film program also screens classics or hard to find movies at very modest ticket prices of $0-10.
With all this--and $10 flat rate parking--I don't know why museum attendance is in decline. It is a great value in terms of cost and quality of experience.