You always will need at least one Custom Post Type (In your case maybe “Courses”) and at least one category within that.
https://wpgeodirectory.com/docs/places-categories-and-listings/
So all listings need to be at least in one category.
Every WP theme has menu options, so getting additional menu plugins is optional.
The WP search will search your whole site and present results in a simple view.
The GD Search (added with widgets) searches all listings (courses) only and presents them in a better way.
You can choose not to display the maps, or you can choose not to use addresses altogether for your listings. In the last case, you will not be able to search and filter by city, unless you create some extra fields yourself.
Where courses are actually in a physical location, I would use a Custom Post Type with addresses and not use the map.
If you also have on-line courses, you might want to create an extra Custom Post Type that does not require addresses.
I hope this helps.