Comment: I think the main question here is implementation. If it means having country specific -trending article feeds, that is fairly straightforward. I wonder what other ways this could manifest itself? If we start getting into country-specific versions of articles, I think we are creating an extra layer of complexity (beyond language specific) with lower benefits.
Topic on Talk:User Interaction Consultation/Wikipedia by country
Country-specific articles is something the editor communities would have to decide about, and would almost certainly decide against (see WP:POVFORK for the relevant enwiki policy).
Country-specific navigation (main page, sidebar, feeds) might make sense though.
A similar example: the wikime app provides articles by geo location not country: https://itunes.apple.com/us/app/wikime/id286865365?mt=8
Is the idea basically about implementing nearby?