The most convenient would be to use the public parking decks, they are free and it's a short distance to the museum, this will allow you to enjoy window browsing downtown as well.
You can park across the street at Jimmy Madison's or in the Water Street parking garage.
There is limited parking across the train tracks behind museum as well
There is a lot right across from the museum with limited, and timed, parking. There is also "pull up to the curb" parking that is timed and adoring the corner on the side of the museum. There are a couple of parking decks within walking distance and also a metered lot very close. Hope this info helps!
There is no designated lot/deck, but plenty of free and close parking options downtown.
We found that on street parking was most convenient. Watch the time limits though.
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