There's free parking near by but its easiest to just pay to park under the old state Capitol.
There are street meters available. The visitors center just 1 1/2 blocks west on Edwards St. is free. The suggestion to park under the old State Capitol is wrong because the old State Capitol building is downtown Illinois State museum is near the new and current state capitol building.
To be close you can pay the street meters. Or walk a few blocks for free.
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