There is a public parking deck not to far on the same street. Not free but not too crazy.
I was on a Charter bus and didn't see any parking, but there has to be some because Museum is across the street from the Nashville Predators Hockey arena.
There's a parking garage like 2 doors down past the burger spot
It's just about 3 doors down from their entrance you can ask them the number of the garage building and they will let you know I think it is already posted on their website also
There is a parking deck below the museum
We used the SpotHero app to find reasonable parking close by.
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