We strongly recommend public transportation - it’s faster, easier, and better for the environment! However, parking is available at the 81st Street Entrance, between Central Park West and Columbus Avenue. It's open from 8am-11pm. Click on the "entrances and exits" tab on this page for prices and more information: https://www.amnh.org/plan-your-visit
No there is no free parking but their are private parking areas nearby where you can park and walk to the museum.
Do not.
No.
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