You can add a category dropdown to the search bar with the Advanced Search Filters add-on. GeoDirectory core on its own only gives you the keyword and “Near” inputs.

With the add-on active:

1. Go to Places > Settings > Search (use the Settings page of whichever post type you want to search).
2. Find the Categories field in the list of available fields and add it to the search fields.
3. Choose how it should look, for example a dropdown, and set the label visitors will see.
4. Turn on the option to show it in the main search bar if you want the dropdown next to the keyword input. Leave it off to show it in the advanced filters panel that opens from the search bar.
5. Save, then test a search on the front end.

The search bar itself is the GD > Search block or the [gd_search] shortcode, so the dropdown appears wherever you have placed that.

For screenshots of every option, see how to add a filter to the main search bar and the search settings overview.