We are often asked about how the order in which the categories appear in the front-end can be changed. Sadly, for the current moment WordPress itself doesn’t provide a reliable way to do this through the Dashboard. We’re really looking forward to have that possibility at some point in a short-term future, so we can give you an option to manage the order.
There are, however, some plugins that let you set orders for different types of taxonomies, such as categories, tags, and others. The one we recommed is Category Order and Taxonomy Terms Order. You may want to give it a try and see if it suit your needs.