You can park on any of the streets with hourly parking. No permit necessary. A permit will just let you stay all day. There's 2-3 hr metered parking (diagonal spots) if you park near the Franklin Institute which is only a few blocks away from the Academy of Natural Sciences. You may have to circle the block a few times but spots do open up. Download the PPA app & you can refill your meter while you're in the musem if your time is about to run out.
I had someone drop us off and pick us up. It you like take the bus . you can park your car and pay for parking if you like but come a little early to find a spot.
Parking is by permit, which you pay for inside. If your hotel is not far, walk no cost incurred..
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