I spent several days in Shirak Province, a region I consider to be one of Armenia's least accessible. Consisting primarily of mountains and high plateaus, and bordered by Georgia to the north, Turkey to the west, and Mount Aragats to the south, Shirak Province is particularly wild and rugged, and unexplored by tourists. Because this is a very rural area and its inhabitants speak with a distinctive accent, it has acquired a reputation for being something of an old-fashioned, backwards region, and the rest of the country mock it for its customs and local culinary specialities (in particular, the Armenian national dish Khash – a kind of broth prepared using cow's feet – comes from here).
Though the region is quite inaccessible and has no major tourist sites, it's a pleasant place to come to spend a break and get away from it all for a while. I especially recommend its capital, Gyumri: with all its grand avenues, it's a particularly enjoyable place to visit.