MILLIE was performed at the Starlight Theatre in Kansas City. It has been there forever and has a long history of summer musical theatre and concerts under the stars.
The problem is the sun is still up when these shows start and in some cases it makes it very disconcerting. For instance, when A CHORUS LINE toured through K.C. you could see people in line for the bathroom or waiting for concessions in the mirrors on the set.
Also, being an outdoor theatre, there was no way to escape CATS when my friends wanted to stay. It was so loud I even heard it in my car in the parking lot.
And, to answer your other question, no, not all tour stops in Kansas City are out doors. This is the only professional venue that is not enclosed.
PEACE.