RE: Will the enhanced categories extension allow me to display categories in a sidebar?
The Widget Pack has a categories widget which will allow you to display the categories as a list in the sidebar.
RE: I want to have a select number of businesses displayed in the sidebar.
The Widget Pack also has a widget to display an entry list in the sidebar. The list is configurable so you can limit by category. The list display the entry name and optionally the logo or photo. The name can optionally be a link to the entry profile page.
Hope this helps!