Whether or not they're still inhabited by people who have chosen a devout way of life, convents have a calming ambiance to them. Visit Convent of the Virgins and feel its spirituality.
You'll have sightseeing choices galore when visiting Kars. Convent of the Virgins is a great place to begin here, but there are lots of other worthwhile sights to consider. Ani, Ani Cathedral, and Small Hamam are close to the community of nuns and will top off your day nicely.