Is there a way to hide the OneDrive option when using the File Open dialog in Office for Mac 2016? I don't store anything in OneDrive, and I always have to switch to "On My Mac", which is irritating when you are constantly doing it.
This helped me:
In the menu of your Office 2016 application, go to Excel (or Word) > Sign out (just below Settings) to log out from OneDrive. Now OneDrive should be gone as a storage option until you log on back to your Microsoft account again using the Add place option.
Note: I am using the German version. The English menu entry might in fact not be Sign out, but Log out or even just Account, but it should work as described. (Maybe someone can edit this answer to fill in the correct words.)