Why do I have categories to break down the events into, but nowhere for my users to click on a specific event category listing and see all events in that category? Is that a link that I have to create and add myself?
The categories for a particular event are shown by default on each single event post – visitors can then click and visit the corresponding archive page as they would with regular WordPress posts.
You can also build a custom menu of event categories from the Appearance > Menus admin screen – just be sure to select Event Categories from the screen options dropdown on that same screen.