Wine
This being Armenia's wine country, you can buy wine in huge jugs on the side of the road, or bottles from a winery. You can also buy young wine, which is not very fermented yet, called majar.
Yeghegnadzor Buried Cheese
This traditional cheese is made nowhere else in the world. Goats milk and herbs are mixed and sealed in a clay pot and buried in the mountains for 6 months, at which point it is salty and sharp. Cheese connoisseurs love this, and you can buy some to take with you.