I went there last week. Parking is $12 for everyone, flat fee. They do not have free parking unfortunately. There is also a fee to visit the Natural History Museum but prices are reasonable and well worth the visit. Same parking fee if you go to the California Science center next door ( $12 parking) except that the California Science Center has free admission. Some people park outside in the streets but I would recommend parking directly there and paying because it is safer. Some places around Exposition Park are not the best areas to park a car.
Parking is 18 flat only thing you have to pay for
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