I have used ACF – Advanced Custom Fields for this multiple times ( http://www.advancedcustomfields.com/resources/how-to-get-values-from-a-taxonomy-term/ ). The problem with taxonomy images & other custom fields is that the values are stored in wp_options table. In bigger sites this will populate the wp_options table a lot and is probably not the most efficient way to store data. You can use advanced techniques to avoid this, but if your site is relatively small, it’s okay to use custom fields the way ACF and categories images -plugin (mentioned in answer by lacey tech solutions) do.
