Yes absolutely, all you have to do is drive up to the main gate tell the guard you are going to the museum. They will ask you for your driver's license and maybe your insurance. Then they will give you directions to the museum. Its actually pretty easy, all the Marines are very friendly. Once you are on base you can pretty much go anywhere you want. They are more relaxed than you might think. It was a great experience, I highly recommend going. If you want they have a junior recruit program(a treasure hunt of Marine Corps history) in the museum that if you finish they give you a really cool patch. Out side of the museum on base don't miss the parade deck where all the new Marines graduate. And the famous yellow footprints are just down the street from the museum as well.
My wife & I had no problem going on base a couple of days before our son's graduation & visiting the museum. Best not to go during graduation time, the museum personnel get a little impatient with the crowds.
You can, but it mostly determines which area you're trying to enter. I believe you have to be there for the marine ceremonies to have access half the time.
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