Are the gardens open even if the indoor museum is closed, I.e.would it be free?
Yes there are
I have found that they leave the gate up during the days when it is closed so that locals can picnic on the grounds...
No, I don't think that it would be free since you have to pay for the park entrance at the very... well, entrance to the park. The garden and the museum are included in the price of the admission, and you may choose to go to the museum or to skip it.
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