Would you file under the "C's for City of or would you file using the name of the city first, then City of?

As long as you're consistent, you could file it either way.

I would personally file it "City of Bloomington", "City of Chicago", "City of Denver", etc.

Which comes first, Dr. Pane Glass Repair or Pane Glass Repair

Which comes first, Dr. Pane Glass Repair or Pane Glass Repair

In alphabetical filing, which comes first, Dr. Pane Glass Repair or Pane Glass Repair

in alphabetical filing, which comes first, Dr. Pane Glass Repair or Pane Glass Repair
Chicago, City of (always the important word first)

Pane, Dr.
Pane Glass Repair

Bamenda, city of