Vanity comes with support for drop down menus off the main menu. You can see an example in the sample store where the Category menu item has a drop down menu underneath containing links to the "Frames" and "Mirrors" collections.
To create a sub-menu, go into Shopify Admin > Navigation, and created a new Link List. The name must match the top level item (e.g. I used "Category" for the demo store).
You can create as many sub-menus as you like.