Park in the O'Donnell Park structure on the corner of Michigan and Lincoln Memorial. You can have parking validated at the museum to get a discount. The parking structure is connected by an elevator.
There is a parking structure that is connected to betty brinns or on the street if you are lucky enough to find one.
There is also road parking along Wisconsin Ave and Prospect, as well as other nearby side streets. Juneau Park is also just to the north, so parking along there and walking might be a good option as well. It's located in a pretty good part of the city for walking from place to place and seeing the sights.
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