In order to restore / backup a Region, you'll need to backup either the Documents\SimCity 4\Regions
folder, or one of the individual region's folders within the Regions
folder. If you've used any plugins when creating your region, you should also backup the Documents\SimCity 4\Plugins
folder.
One important thing to note though, is the distinction between regions and cities. A city is made up of a single tile, where as a region is made up of one or more city tiles. The reason why this distinction is important is because whilst it is possible to restore an entire region (meaning all its cities) simply by copying and pasting the region's folder from your backup, it is not possible to restore a single city tile within the region due to the way Simcity 4 handles save games.
In other words, if you've accidentally flattened one of your cities or a city has become corrupted (perhaps due to bugs associated with using the "Save and..." options), the only way to restore that one, single city tile, is to restore the entire region from backup.