Adding a Link to Display Sub Categories and Search

I’m using the Grid layout, which seems to work best with my theme. It lists however many categories that I tell it to…

If you click on Restaurants for example, it will display every restaurant, regardless of their sub-category. Is there a way or a shortcode available that will display the Sub-Categories of a category only? So if i went to Restaurants, it would show the 10 or so sub categories?

I think I’m finding that although I can organize the category structure, I really can’t take full advantage of it.

Also what about a search bar of some sort for the items in the Directory?