You can park on Clark, walk over, it's not far. Parking meters on Clark take credit debit & cash. This nature museum won't keep you terribly long to enjoy.
I drove in circles until I found parking... over 30 minutes. I recommend public transport.
Take public transport instead of driving. The 151 bus stops like a block away.
There is a paid lot across the street, but fairly expensive. I think it might be $25+ to park there. If you are a member of the Lincoln Park zoo you can park at the zoo for a discount or free, depending on your membership level. There is also meter parking on the nearby side streets if you are willing to walk a few blocks. If you are only spending an hour or two, this is probably the best way.
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