The Museum of Natural History has a pay and display lot on site which is administered by Indigo Parking. This is a public lot and is frequently used by museum visitors and those visiting the area. Parking is $3.00 per hour. The machine accepts coins and credit cards. You can also pay using the Indigo Neo app. You will need to enter your license plate number during the transaction.
In addition to the Museum's parking lot, here are numerous on-street pay stations that allow for payment by coin, debit card, credit card, and smartphone.