yes, they have
Side and front...
The National Museum of Mexican Art now has a parking lot. The rate is $2/hour.
During special events like Dia De Los Muertos, it's very hard. You could park blocks away. Maybe on a regular visit you can.
Yes on the side of the museum
Plenty of free Street parking. There is metered parking lot on the West side of the museum, run by the park district.
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