GeoDirectory category pages are generated, so they have no Featured Image box like a normal page. You can still show an image at the top of each category page, either a different one per category or the same one on all of them.

A different image for each category

1. Go to Places > Place Categories and edit a category.
2. In Category Top Description, add the image with the Add Media button, plus any text you want.
3. Update the category and repeat for the others.

The top description is shown by the GD > Category Description block, which is on the Archive page template by default. If you removed it, add it back to the page set as Archive page at GeoDirectory > Settings > General > Pages.

The same image on every category page

Edit the Archive page template and add an Image block (or a Cover block with your heading) above the listings. Every category page uses this template, so the image shows on all of them.

Using the category’s Default Listing Image

Each category also has a Default Listing Image field. It is used for listings in that category that have no photos, as the background in the GD > Categories image design, and as the social sharing image for the category page. With Elementor Pro you can show it at the top of a GD Archive template with the GD Image Field dynamic tag set to the category image.

Featured image from your theme

Some themes show a header image on archive pages from their own settings. If your theme does, look in its customizer options for archive or category headers. That part is controlled by the theme, not by GeoDirectory.