The settings page in events contains a tab called "Navigation" - this is where you can edit the public events top navigation bar:
You can create multiple navigation lists, but only one navigation list can be used on the public events page since there is only one site, and one top navigation bar. After creating a navigation list, you are redirected to the navigation editor:
Simply drag & drop to determine the links that will go in the top nav-bar.
There are 5 options for links
Today (pre-built link)
Featured (pre-built link)
Upcoming (pre-built link)
New Internal Link
Internal links can be used to create nav bar links for specific filters, such as link that automatically goes to the "Alumni Events" filter.
New External Link
The navigation list that is displayed on the public events site is set on the "Website" settings page: