I would say your solution of providing a second level of filters based upon the primary filter would work best as it allows the user to establish the primary hierarchy (which is the country name) and the relational mapping which is the region name allowing him to drill down from a higher level to a lower level as needed.
How you would do that would depend on whether you are planning to allow multiple sub filters at that level. If you are planning to just allow filtering by say one region, then links would work best else checkboxes would work fine.
To quote this article from UX Matters :
There are two basic ways of selecting values for filters: drill-down
and parallel selection. Ignoring the various modalities of the many
derivative mechanisms for these primary modes of selection, the two
basic ways of specifying a value for a filter essentially boil down to
two choices: links and check boxes.
A link is the simplest mode of filter selection. By clicking a link, a
customer can either select a single value for a specific filter or
drill down a level in a taxonomy, like a category or department
hierarchy. Amazon.com, shown in Figure 1, provides one of the best
examples of a search results user interface that uses links to
indicate filter value selections. Links usually indicate a
straightforward equals condition—for example, I want to narrow my
search results to Department = Books—as they do on Amazon.
The use case there is where you are looking to help the user exclude other branches in the taxonomy entirely. This is good for very deep sites.
However if you are looking allowing multiple sub filters, This is also done pretty well by Volkswagon which provides faceted search to filter down based upon Models by providing multiple checkboxes