I have been to the Smithsonian Air & Space Museum when I was a kid.. My kids haven't been to that one, but they have been to the (not free) one in Newport News area a few times! I think that one is actually even better. :-)
My kids have been to visited probably over 30 museums in 5 different states! :-b We love our museums!
But we've been to the Naval Aviation Museum on the base in Pensacola, FL - it's pretty impressive and totally FREE.
We also went to the Smithsonian Museum of Natural History last summer. We had a couple of hours to spend in D.C. so we went to Arlington National Cemetery (also free, and I enjoyed it, but less interesting to young children), then left our car parked there and took the train over to DC and went to the Natural History museum for about an hour. We could easily spend a week in D.C. going to all the free museums but we just didn't have the time.
We live close.to Getty center (well here close is about an hour drive) and we haven't made it up there! I planned a whole fancy art curriculum last year and planned to do one museum, including the Getty) every other month and we got busy doing other things.
I have been to Forest Lawn, Glendale. My Grandma is buried there. They have amazing art and hardens. They put on free history programs as well. We go at least once a year. I would recommend it if you have tome in the Los Angeles area! (Though it is kinda odd the first time since it is in a cemetary..lol)
My oldest son did a tour of the East coast with Boy Scouts. I have pics of him on the Constitution, they went to the Smithsonian,hit many of the great national landmarks including participating in laying a wreath at Arlington.
Yes, I have been to the Getty Center and Forest Lawn. It is nice to see Forest Lawn on this list because I am always recommending it to people...but they are reluctant to go because the first thought that comes to mind is that it is a cemetary. But it is so much more than that.