There are parking garage close by though all do cost.
Union station has parking, and there are several city buildings nearby that often allow people to park if you get permission first.
Well, not knowing your particulars, it is a train station with extended parking options. Not sure what a week would cost. Check parking at 2 hotels attached to Union Station.
There is covered parking at Union Station but it's $12 per night. I'm not sure how close you can do public parking for free.
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