Questions: Your theme seems to work perfectly except the featured categories on homepage.
I’ve checked the categories listing edition of the homepage through the administration, everything seems to be seted and behave as expected, however nothing shows up on the homepage still.
My Answer: The Featured category is missing caused by the Featured image is lost or blank, please go to:
CityBook Listings > Listing Categories, Edit your Category and upload image to set its Featured image
This is How it looks on Front-end: