Their website recommended LaSalle garage
I prefer to park in the 10th and Hennepin ramp, which is directly across Hennepin from the theatre. The current event parking rate is $9. The only drawback to parking in the ramp is that is takes 15-20 minutes to exit once the show is over. But if you plan to grab something to eat at a restaurant before leaving downtown, that won't be a problem.
There are multiple ramps nearby. Street parking if you can find it amd street lots. All pay parking
Multiple ramps within a 2 block area. Cheap after 4pm
Hawthorne Ramp on 1st; LaSalle ramp; ramp at 11th & Harmon Place - 3 good fair-priced ramps. There are surface lots near but $$ for events.
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