List of categories/assign groups to categories

Is there a way to add a menu item that would show a list of categories? Ir failing that, a way to assign groups to a specific category?

My website is broken down into US regions, i.e., Northeast, Southwest, etc. Under those categories I'd like to put the individual states within the region. To make things easier for people I'd like to have a drop-down where they can just click whatever region they're in, then see the groups within that category.

Blogs and so on can be placed in a category but apparently a group can't? Can I also assign groups to a category? Thanks for any help!