Parking is not free. There is a parking lot, but there is a charge. Some nearby streets have meters, others have parking restrictions. Just read the posted signs. There is the option of the Exposition train line. It has several stops along the length of Exposition Park.
Free and check Groupon for special exhibit tickets.I found some for 50% off
The California Science Center is free! But if you want to see any of the special exhibits you need tickets for that. You can check the prices for current exhibits here. https://californiasciencecenter.org/visit/admission/get-tickets If you decide just to do the free part is still really fun.
Each special exhibit has its own price. But they should be listed on there website.
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