Is there public parking nearby?

Yes there is around the corner.

There is either on-street metered parking or nearby public parking ramps. But the museum is connected to the skyway system.

We paid for a parking garage. Street parking is hard to find.

There are two other options. Take the Green Line to the Central Station and walk half a block and the 94 bus also stops on the corner of Robert and 5th. Both options are cheaper than paying for parking.