Here is the demo for the WordPress.com version of the Suburbia theme:
http://suburbiademo.wordpress.com/

I looked at your blog and I did see that you have added the categories widget to your right column on single posts:
http://styleinmycity.com/2012/09/29/iheartstalbans/

But were you talking about the home page? Note that there is not a way to add the categories widget below the menu on the WordPress.com Suburbia theme home page (top left), but one thing that may help would be to link to a few categories in the menu itself. You can do that with a custom menu if you'd like, see this help page for details:
http://en.support.wordpress.com/menus/

I have been searching for hooours as to how I can move/add the category list to the right column, to sit under the pages. In the Surburbia demo, it's there, but I cannot find out where to configure this myself.

Help would be much much appreciated!
Thanks!