You can park in the garage under the museum. Just be sure to get a validation when you get your ticket to the museum. It doesn't cover the whole cost of the parking but it does reduce it.
Standard for downtown - parking garages or paid street parking (free on weekends)
Parking in the garage behind the museum. Weekend only.
On the street, if you are lucky. Otherwise, look for a nearby garage.
There is public parking in the weekend
Park at Target across the street. If you spend $20 at Target you get 2 hours free parking.
No public parking nearby
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