Diana L. answered 04/27/20
Experienced and Innovative Tutor for Test Prep
Keep the comma and use "appreciate."
The phrase "and the city of Madison" works best as a non-essential clause, meaning that the sentence still makes sense without it. Because it's of secondary importance, this clause needs a beginning and ending comma to set it off from the "essential" part of the sentence.
With that clause set off, you need the verb to agree with "we" and not "Madison."
The bags will be gifted backstage to the performers to let them know just how much we, and the city of Madison, appreciate them.
(You might want to drop the "just"; it doesn't serve a purpose here.)