It is a monastery. Suzdal is the oldest city in Russia, up there with Moscow and Vladimir. These are the oldest and most picturesque cities in Russia. Suzdal is a gem of the pastoral old world. Structures that in the US would have people forming committees to throw money at their restoration too often slowly fall apart.
Churches often have scaffolding inside and out or are closed.
But even with this, this walled city still rings its famous church bells, which quickly came to be my favorite thing. In fact, bell ringing there is considered a kind of art form because of the variety of tempos and harmonies that they have. Its not just one bell that rings, but many. This is the wall that goes around the outside of Suzdal. The day we went was a cool misty day in November.