I just visited a few weeks ago. I believe it was $25+ to park underground at the museum. I was on foot, so it didn't apply to me. I'd suggest parking in the neighborhood (Hyde Park) and walking a few blocks. You'll get to experience a lesser known part of the city. Cross under 57th Street and say hello to John, a homeless & harmless man who has a great view of the MSI!
We used spothero app to find ours for around $15 about a 20 mimute walk. The field's website gives some other options too . http://www.fieldmuseum.org/visit/directions-parking
It has its own parking area and i forgot how much it costs
If private parking is between 10 dollars or more Public primeters are cheaper 3.75 per hour
It has a large parking lot but its always crowded. Might be best to take a cab.
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